## Basic Geometry : How to find the perimeter of a rectangle

## Example Questions

**Example Question #1 : How To Find The Perimeter Of A Rectangle**

Given the rectangle in the diagram, what is the perimeter of the rectangle?

**Possible Answers:**

38 cm

24 cm

40 cm

14 cm

19 cm

**Correct answer:**

38 cm

**Explanation:**

The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:

12+12+7+7=38

The perimeter is 38 cm.

**Example Question #2 : How To Find The Perimeter Of A Rectangle**

One side of a rectangle is 7 inches and another is 9 inches. What is the perimeter of the rectangle in inches?

**Possible Answers:**

63

64

16

32

36

**Correct answer:**

32

To find the perimeter of a rectangle, add the lengths of the rectangle’s four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

(2⋅9)+(2⋅7)=32

**Example Question #3 : How To Find The Perimeter Of A Rectangle**

A rectangle has an area of 96cm2. The width is four less than the length. What is the perimeter?

**Possible Answers:**

80cm

100cm

75cm

60cm

40cm

**Correct answer:**

40cm

**Explanation:**

For a rectangle, area is A=lw and perimeter is P=2l+2w, where l is the length and w is the width.

Let x = length and x−4 = width.

The area equation to solve becomes x(x−4)=96, or x2−4x−96=0.

To factor, find two numbers the sum to -4 and multiply to -96. -12 and 8 will work:

x^{2} + 8x – 12x – 96 = 0

x(x + 8) – 12(x + 8) = 0

(x – 12)(x + 8) = 0

Set each factor equal to zero and solve:

x=12 or x=−8.

Therefore the length is 12cm and the width is 8cm, giving a perimeter of 40cm.

Example Question #4 : How To Find The Perimeter Of A Rectangle

A rancher wants to surround his rectangular field with barbed wire fence that costs $1.75 per foot. The field measures 200 yards by 400 yards. How much will the fence cost?

**Possible Answers:**

$9,450

$3,150

$3.600

$6,300

$2,100

**Correct answer:**

$6,300

Convert the dimensions from yards to feet by multiplying by 3: This makes the dimensions 600 feet and 1,200 feet. The perimeter of this farm is therefore

P=600+600+1,200+1,200=3,600ft.

Multiply this by the cost of the fence per foot:

3,600⋅$1.75=$6,300

**Example Question #5 : How To Find The Perimeter Of A Rectangle**

A rectangle has a length of 20 inches and a width of 12 inches, find the perimeter of the rectangle.

**Possible Answers:**

64 inches

56 inches

40 inches

24 inches

240 inches

**Correct answer:**

64 inches

**Explanation:**

To find the perimeter of any rectangle, add all of the sides up:

20 + 20 + 12 + 12 = 64 inches

You could use this formula as well:

P=2l+2w, where P = perimeter, l = length, w = width

This formula comes from the fact that there are 2 lengths and 2 widths in every rectangle.

P=2(20)+2(12)

P=64 inches

**Example Question #6 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of this rectangle.

**Possible Answers:**

65

87

60

43

20

**Correct answer:**

60

Remember, the perimeter of the rectangle is the sum of all four sides:

P=6+24+A+B

It is obvious from the figure that A=6 and B=24.

P=6+24+6+24=60

**Example Question #7 : How To Find The Perimeter Of A Rectangle**

A rectangle has an area of 56 square feet, and a width of 4 feet. What is the perimeter, in feet, of the rectangle?

**Possible Answers:**

**Correct answer:**36

**Explanation:**

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.

**Example Question #8 : How To Find The Perimeter Of A Rectangle**

The area of a rectangle is 32 in2, and the width of this rectangle is two times its height. What is the perimeter of the rectangle?

**Possible Answers:**

24 inches

8 inches

36 inches

12 inches

32 inches

**Correct answer:**

24 inches

The area of a rectangle is the width times the height, and we are told that in this rectangle the width is two times the height.

Therefore, A=W×H;W=2H.

Plug in the value of the area:

32in2=W×2W=2W2

Solve for W to find a width of 4 inches. Using our formula above, the height must be 8 inches. We then add all the sides of the rectangle together to find the perimeter:

8+8+4+4=24 in.

**Example Question #9 : How To Find The Perimeter Of A Rectangle**

Robert is designing a rectangular garden. He wants the area of the garden to be 9 square meters. If the length of the lot is going to be three meters less than twice the width, what will the perimeter of the lot be in meters?

**Possible Answers:**

10

12

6

1.5

3

**Correct answer:**

12

Let l be the length of the garden and w be the width.

By the specifications of the problem, l = 2w-3.

Plug this in for length in the area formula:

A = l x w = (2w – 3) x w = 9

Solve for the width:

2w²- 3w – 9 =0

(2w + 3)(w – 3) = 0

w is either 3 or -3/2, but we can’t have a negative width, so w = 3.

If w = 3, then length = 2(3) – 3 = 3.

Now plug the width and length into the formula for perimeter:

P = 2 l + 2w = 2(3) + 2(3) = 12

**Example Question #10 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle that has a length of 12 and a width of 3.

**Possible Answers:**

40

45

15

30

**Correct answer:**

30

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(12+3)=2(15)=30

**Example Question #11 : Rectangles**

Find the perimeter of a rectangle that has a length of 20 and a width of 1.

**Possible Answers:**

21

82

66

42

**Correct answer:**

42

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(20+1)=2(21)=42

**Example Question #12 : Rectangles**

Find the perimeter of a rectangle that has a length of 4 and a width of 15.

**Possible Answers:**

38

60

54

19

**Correct answer:**

38

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(4+15)=2(19)=38

**Example Question #13 : Rectangles**

Find the perimeter of a rectangle that has a length of 20 and a width of 15.

**Possible Answers:**

150

300

70

35

**Correct answer:**

70

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(20+15)=2(35)=70

**Example Question #14 : Rectangles**

Find the perimeter of a rectangle that has a length of 16 and a width of 10.

**Possible Answers:**

26

52

78

160

**Correct answer:**

52

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(16+10)=2(26)=52

**Example Question #25 : Rectangles**

Find the perimeter of a rectangle that has a length of 4 and a width of 16.

**Possible Answers:**

64

10

40

60

**Correct answer:**

40

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(4+16)=2(20)=40

**Example Question #26 : Rectangles**

Find the perimeter of a rectangle that has a length of 64 and a width of 36.

**Possible Answers:**

154

264

200

100

**Correct answer:**

200

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(64+36)=2(100)=200

**Example Question #17 : Rectangles**

Find the perimeter of a rectangle that has a length of 6 and a width of 0.5.

**Possible Answers:**

3

6.5

13

26

**Correct answer:**

13

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(6+0.5)=2(6.5)=13

**Example Question #28 : Rectangles**

Find the perimeter of a rectangle that has a width of 87 and a length of 21.

**Possible Answers:**

108

264

332

216

**Correct answer:**

216

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(87+21)=2(108)=216

### Example Question #11 : How To Find The Perimeter Of A Rectangle

Find the perimeter of a rectangle that has a length of 53 and a width of 19.

**Possible Answers:**

72

96

144

182

**Correct answer:**

144

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(53+19)=2(72)=144

**Example Question #12 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle that has a width of 10 and a length of 12.

**Possible Answers:**

48

44

22

52

**Correct answer:**

44

Recall how to find the perimeter of a rectangle:

Perimeter=(2×width)+(2×length)

For the given rectangle,

Perimeter=(2×10)+(2×12)=20+24=44

### Example Question #21 : How To Find The Perimeter Of A Rectangle

Find the perimeter of a rectangle that has a length of 14 and a width of 16.

**Possible Answers:**

90

60

45

30

**Correct answer:**

60

Recall how to find the perimeter of a rectangle:

Perimeter=2(length+width)

For the given rectangle,

Perimeter=2(14+16)=2(30)=60

**Example Question #22 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 35, and the length of the rectangle is 5, what is the perimeter of the rectangle?

**Possible Answers:**

36

18

24

12

**Correct answer:**

24

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(5+7)=24

**Example Question #23 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 106, and the length of the rectangle is 2, what is the perimeter of the rectangle?

**Possible Answers:**

120

130

110

100

**Correct answer:**

110

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(2+53)=110

**Example Question #24 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 96, and the length of the rectangle is 16, what is the perimeter of the rectangle?

**Possible Answers:**

44

52

40

48

**Correct answer:**

44

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(16+6)=44

**Example Question #25 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 16, and the length of the rectangle is 4, what is the perimeter of the rectangle?

**Possible Answers:**

16

20

12

24

**Correct answer:**

16

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(4+4)=16

**Example Question #26 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 36, and the length of the rectangle is 4, what is the perimeter of the rectangle?

**Possible Answers:**

26

30

22

34

**Correct answer:**

26

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(4+9)=26

**Example Question #27 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 20, and the length of the rectangle is 4, what is the perimeter of the rectangle?

**Possible Answers:**

18

14

22

10

**Correct answer:**

18

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(4+5)=18

**Example Question #28 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 215, and the length of the rectangle is 5, what is the perimeter of the rectangle?

**Possible Answers:**

102

106

96

90

**Correct answer:**

96

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(5+43)=96

**Example Question #29 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 148, and the length of the rectangle is 4, what is the perimeter of the rectangle?

**Possible Answers:**

78

74

86

82

**Correct answer:**

82

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(4+37)=82

**Example Question #30 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 150, and the length of the rectangle is 30, what is the perimeter of the rectangle?

**Possible Answers:**

70

80

60

90

**Correct answer:**

70

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(30+5)=70

**Example Question #31 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 180, and the length of the rectangle is 10, what is the perimeter of the rectangle?

**Possible Answers:**

44

56

54

28

**Correct answer:**

56

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

width=Area/length

Plug in the information from the question to find the width of the rectangle.

Width=180/10=18

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(10+18)=56

**Example Question #32 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 200, and the length of the rectangle is 50, what is the perimeter of the rectangle?

**Possible Answers:**

116

108

104

112

**Correct answer:**

108

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

width=Area/length

Plug in the information from the question to find the width of the rectangle.

Width=200/50=4

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(50+4)=108

**Example Question #33 : How To Find The Perimeter Of A Rectangle**

If the area of a rectangle is 256, and the length of the rectangle is 32, what is the perimeter of the rectangle?

**Possible Answers:**

80

72

88

96

**Correct answer:**

80

Recall how to find the area of a rectangle:

Area=length×width

Now, we can use this equation to find the width of the rectangle.

width=Area/length

Plug in the information from the question to find the width of the rectangle.

Width=256/32=8

Now, recall how to find the perimeter of a rectangle.

Perimeter=2(length+width)

Plug in the length and width values to find the perimeter.

Perimeter=2(32+8)=80

**Example Question #34 : How To Find The Perimeter Of A Rectangle**

If the area of this rectangle is 160, what is the perimeter?

**Possible Answers:**

60

28

52

26

**Correct answer:**

52

Explanation:

In order to find the perimeter of a rectangle, you will need to know both length and width. The question, however, only provides us with the width.

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=160/16=10

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(16+10)=2(26)=52

**Example Question #35 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 180, what is the perimeter?

**Possible Answers:**

56

40

48

64

**Correct answer:**

56

In order to find the perimeter of a rectangle, you will need to know both length and width. The question, however, only provides us with the width.

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=180/18=10

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(18+10)=2(28)=56

**Example Question #36 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 600, what is the perimeter?

**Possible Answers:**

224

106

318

212

**Correct answer:**

212

In order to find the perimeter of a rectangle, you will need to know both length and width. The question, however, only provides us with the width.

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=600/100=6

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(6+100)=2(106)=212

**Example Question #37 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 74, what is the perimeter?

**Possible Answers:**

78

70

85

69

**Correct answer:**

78

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=74/27=2

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(37+2)=2(39)=78

**Example Question #38 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 64, what is the perimeter?

**Possible Answers:**

36

40

54

48

**Correct answer:**

40

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=64/16=4

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(16+4)=2(20)=40

### Example Question #39 : How To Find The Perimeter Of A Rectangle

If the area of the rectangle is 72, what is the perimeter?

**Possible Answers:**

16

44

36

24

**Correct answer:**

36

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=72/12=6

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(12+6)=2(18)=36

**Example Question #40 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 60, what is the perimeter?

**Possible Answers:**

54

64

44

34

**Correct answer:**

34

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=60/12=5

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(12+5)=2(17)=34

**Example Question #41 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 168, what is the perimeter?

**Possible Answers:**

40

52

46

60

**Correct answer:**

52

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=168/12=14

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(12+14)=2(26)=52

**Example Question #42 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 600, what is the perimeter?

**Possible Answers:**

100

130

190

160

**Correct answer:**

100

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=600/20=30

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(20+30)=2(50)=100

**Example Question #43 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 228, what is the perimeter?

**Possible Answers:**

62

148

124

31

**Correct answer:**

62

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=228/12=19

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(12+19)=2(31)=62

**Example Question #44 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 128, what is the perimeter?

**Possible Answers:**

48

54

56

42

**Correct answer:**

48

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=128/8=16

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(16+8)=2(24)=48

**Example Question #45 : How To Find The Perimeter Of A Rectangle**

If the area of the rectangle is 1440, what is the perimeter?

**Possible Answers:**

152

324

168

204

**Correct answer:**

152

Recall how to find the area of the rectangle:

Area=length×width

Now, using the area and the given width, we can then find the length.

length=Area/width

Plug in the given values.

length=1440/36=40

Now that we have both length and width, find the perimeter of the rectangle.

Perimeter=2(length+width)

Perimeter=2(36+40)=2(76)=152

**Example Question #46 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle given width 4 and length 6.

**Possible Answers:**

20

12

10

24

**Correct answer:**

20

To solve, simply use the fomula for the perimeter of a square. Thus,

P=2(w+l)=2∗(4+6)=2∗10=20

**Example Question #47 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle given width of 6 and length of 8.

**Possible Answers:**

24

48

28

56

**Correct answer:**

28

The perimeter of a rectangle is found by adding all the side lengths together. In a rectangle there are two widths and two lengths.

In other words, simply use the formula for the perimeter of a rectangle and let,

w=6l=8.

Thus,

P=2(w+l)=2∗(6+8)=2∗14=28

**Example Question #48 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle with width 9 and length 1.

**Possible Answers:**

9

20

10

18

**Correct answer:**

20

To solve, simply use the formula for the perimeter of a rectangle. Thus,

P=2(w+l)=2∗(9+1)=2∗10=20

**Example Question #49 : How To Find The Perimeter Of A Rectangle**

A Quidditch field is rectangular in shape and boasts a width of 30yd (yards) and a length that is 10yd short of three times the width. Given this information, what would be the perimeter of the field?

**Possible Answers:**

220yd

300yd

240yd

120yd

110yd

**Correct answer:**

220yd

To solve for the perimeter of the Quidditch field, we must first determine the length of the field. With the provided information, we can solve for this by drafting an algebraic equation:

length=3(width)−10yd=3(30yd)−10ydlength=90yd−10yd=80yd

Now that we know our length, we can determine the perimeter of the field:

Perimeter=80yd+80yd+30yd+30yd=220yd

**Example Question #50 : How To Find The Perimeter Of A Rectangle**

A football field is rectangular in shape. The length of the field is 100 yards and the width of the field is 50 yards. What is the length of the perimeter?

**Possible Answers:**

300yards

200yards

5000yards

500yards

150yards

**Correct answer:**

300yards

A rectangle has the same length on either side and the same width on either side. Therefore if the football field has 100 yards in length and 50 yards in width you can use this formula.

2l+2w=p

(2∗100)+(2∗50)=

200+100=

300yards

**Example Question #51 : How To Find The Perimeter Of A Rectangle**

Find the perimeter of a rectangle given length 7 and width 2.

**Possible Answers:**

14

49

28

18

**Correct answer:**

18

To solve, simply use the formula for the perimeter of a rectangle. Thus,

P=e(l+w)=2∗(7+2)=2∗9=18

If the formula escapes you, simply draw a picture and add all of the sides together. Rememeber, a rectangle has 4 sides, two are equal and the other 2 are equal.

**Example Question #52 : How To Find The Perimeter Of A Rectangle**

A rectangle has an area of 27cm2. The rectangle’s sides have values of xcm and 3xcm. What is the perimeter of the rectangle?

**Possible Answers:**

24cm

3cm

9cm

12cm

30cm

**Correct answer:**

24cm

First, we must solve for x. The formula for the area of a rectangle is A=lw. Because we know the area is 27, and the length and width are x and 3x, we can plug these in to solve for x, as follows:

A=lw

27=x(3x)

27=3x2

x=3

Since we know that x=3, we can use this to solve for the sides of the rectangle:

l=x

l=3

and

w=3x

w=3(3)

w=9

We can now use these values to solve for the rectangle’s perimeter:

P=2(l+w)

P=2(3+9)

P=2(12)

P=24cm

Therefore, the perimeter of the rectangle is 24cm.

**Example Question #53 : How To Find The Perimeter Of A Rectangle**

A rectangle has an area of 36cm2. What is the perimeter of the rectangle?

**Possible Answers:**

12cm

Not enough information is given.

48cm

24cm

6cm

**Correct answer:**

Not enough information is given.

Not enough information is given to solve this problem. While 24cm2 is a possible answer (assuming all of the sides of the rectangle are 6cm), because it is a rectangle, you cannot assume that all of the sides are the same. Because 36 is not a prime number, there is more than one combination of numbers that could work out to equal an area of 36cm2.

**Example Question #54 : How To Find The Perimeter Of A Rectangle**

Horton’s Tile and Fixtures cuts Spanish tile in a rectangular shape that is 15cm wide and has an area of 315cm2. What would be the perimeter of a cut Spanish tile?

**Possible Answers:**

72cm

68cm

74cm

80cm

62cm

**Correct answer:**

72cm

Since we know the width and area, we can determine the length by using the equation for area of a rectangle:

area=length⋅width315cm2=length⋅15cm

Now that we know the length of the tile, we can solve for perimeter:

perimeter=2l+2w=2(21cm)+2(15cm)=42cm+30cm=72cm

**Example Question #55 : How To Find The Perimeter Of A Rectangle**

If the length of a rectangle is 2 inches longer than the width, and the width is 4–√ , what is the perimeter of the rectangle?

**Possible Answers:**

12in

8in2

20in

8in

12in2

**Correct answer:**

12in

First we need to know that the square root of 4 is 2, we can know this because because if we work backwards we see that 2 x 2= 4, so we know the width of the rectangle is 2.

Since the length is 2 more than the width, we add 2 + 2 and get a length of 4 inches.

2+2=4

Now we can draw the rectangle and label each width (short side) with a measure of 2 inches and each length (long side) with a measure of 4 inches.

Now all we need to do is add up all the sides, so we have 2 + 2 + 4 + 4 which equals 12.

P=2+2+4+4P=12

Since we are adding, and the measurements are in inches, our answer is 12in.

## Perimeter of Rectangle

**Perimeter of Rectangle** could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. In Maths, you will come across many geometric shapes and sizes, which have an area, perimeter and even volume (for 3-d figures). You will also learn the formulas for all those parameters. Some of the examples of different shapes are circle, square, polygon, quadrilateral, etc. In this article, you will study the key feature of the rectangle, i.e. perimeter.

Perimeter basically gives the length of the figure. Suppose for a square, which has all its sides as equal, the perimeter of the square will be four times its sides. In the case of a circle, the perimeter is termed as circumference, which is calculated based on its radius. Before we find out the perimeter of a given rectangle, let us learn first, what a rectangle is.

A rectangle is a quadrilateral that has two pairs of parallel sides equal and all the four angles at the vertices are right angles.

## What is Perimeter of Rectangle?

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of rectangle will be in meters, centimeters, inches, feet, etc.

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and has the same linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

- All four angles of a rectangle are 90°.
- The opposite sides of a rectangle are equal in measure.

Imagine a rectangular park in your neighborhood. Have you ever thought about how long its boundary is?

If you go around the park along its boundary once, you cover a distance. This distance is the **perimeter **of the park. In order to measure the perimeter of any rectangular field, you travel along the boundary of the four sides of the field. You begin at a fixed point called the starting point and end when you reach the starting point again. This length or distance of the boundary is called the perimeter of a rectangle.

## Perimeter of a Rectangle Formula

**The perimeter of a rectangle is defined as the sum of all the sides of a rectangle**. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”. Let us derive the formula for its perimeter and area.

Suppose a rectangle has length and width as b and a, respectively.

From the definition of the perimeter we know, the **perimeter of a rectangle, P = 2 ( a+b) units**

where

“a” is the length of the rectangle

“b” is the breadth of the rectangle

The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w) units, where ‘l’ is the length and ‘w’ is the width of the rectangle. Let us understand this with the help of a simple example. David wants to put a fence around his farm so that his sheep will not wander away. Let us now understand this formula with an example. He wants to know how much wire he would need to put a fence around his rectangular farm.

Let us first name the sides of his farm. The larger side of this rectangular farm is named (l). The smaller side is named (w). Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter. Total distance = l + w + l + w = 2l + 2w. Therefore, the Perimeter of the rectangle = 2(l + w).

## Derivation of Perimeter of Rectangle

Since the perimeter is equal to the sum of all the sides of the polygon. Hence, in the case of a rectangle, the perimeter (P) is;

P = sum of all its four sides

P = a + b + a + b (Opposite sides of rectangle are equal)

P = 2(a + b)

Hence, derived.

Therefore,

Perimeter of a rectangle = 2(Length + Width) square units |

Now let us write the formula for the area of a rectangle, with respect to same above given figure;

Area of a rectangle = Length × Width = a × b |

## Applications of Perimeter of Rectangle

There are many real-life applications of the perimeter of a rectangle. A few of them are listed below:

- We can determine the length of a rectangular field or a garden for its fencing using the perimeter formula
- It can be used for many art and craft projects such as decorating the border of rectangular cardboard with colourful ribbons or ropes
- For the construction of a rectangular swimming pool, the length of swimming races are defined by the perimeter
- For the construction plan of the house, we need to set a boundary using concrete that is possible by perimeter formula

## Perimeter of a Rectangle

Rectangles are four-sided polygons. Following are the properties of a rectangle:

**(i)** All the angles of a rectangle are 90º.

**(ii)** Opposite sides of a rectangle are always the same in size.

## Perimeter of a rectangle

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle.

Perimeter of the given rectangle is a + b + a + b. Since opposite sides of a rectangle are always equal, we need to find the dimensions of only two sides to find the perimeter of a rectangle.

The perimeter of the above rectangle with sides ‘a units’ and ‘b units’ is:

a + b + a + b = 2a + 2b = 2 (a + b) units.

Hence, the formula for the perimeter of a rectangle = 2 × (sum of adjacent sides)

**Examples of finding the perimeter of a rectangle**

**Example 1**. The two sides of the rectangle are given. What will be the perimeter of the rectangle?

**Solution**: One side of the rectangle is 2 cm and the other side is 5 cm.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangle = 2 × (5 + 2) = 2 × (7) = 14 cm

**Example 2**. A rectangular playground is 20 m long and 13 m wide. Find its perimeter.

**Solution**: One side of the rectangular playground is 20 m and the other side is 13 m.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangular ground = 2 × (20 + 13) = 2 × (33) = 66 m

**Tricky problems involving perimeter of rectangles**

**Type I**: When the perimeter and only one of the sides are given.

**Example 1**. If the perimeter of the given rectangle is 10 cm and the length of one of its sides is 2 cm. What will be the other side?

**Solution**: The perimeter of the rectangle, with one of the sides equal to 2 cm, is 10 cm.

Let the missing side be ‘a’.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

10 = 2 × (2 + a) 5 = (2 + a)

a = 5 – 2 = 3 cm

**Type II**: Finding sides using the properties of a rectangle.

Example 2. In the given rectangle, if a = 4 cm and d = 3 cm. Find b and c.

**Solution**: We know that side a = 4 cm and side d = 3 cm.

To find side b and c, we use the property that the opposite sides of a rectangle are always the same in size.

Hence, a = c = 4 cm and d = b = 3 cm.

Fun FactsMany historical buildings have rectangle like shapes in them e.g. Parthenon in Athens. |

## Usage of Perimeter of a Rectangle

The Perimeter of a rectangle makes things easier and helps us in calculating distances and lengths in our day-to-day lives.

For example,

- If you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter.
- If you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need.

## Solved Examples on Perimeter of Rectangle

**Q.1:** **Find the perimeter of a rectangle whose length and width are 5 cm and 10 cm, respectively.**

**Solution:** Given:

Length = 5 cm and Width = 10 cm

We know,

The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(5 + 10) cm

P = 2 x 15 cm

Therefore, the perimeter of a rectangle = 30 cm

**Q.2: Find the perimeter of a rectangle whose length and breadth are 12 cm and 15 cm, respectively.**

Solution:

Given:

Length = 12 cm and Breadth = 15 cm

We know,

The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(12 + 15) cm

P = 2 x 27 cm

Therefore, the perimeter of a rectangle = 54 cm

**Q.3: A rectangular yard has length equals to 10 cm and perimeter equals to 60 cm. Find its width.**

**Solution:** Given,

Perimeter of the yard = 60 cm

Length of the yard = 10 cm

Let W be the width of the yard.

From the formula, we know,

Perimeter, P = 2(length + width)

Substituting the values, we get;

60 = 2(10 + width)

10 + W = 30

W = 30 – 10 = 20

Hence, the width of the yard is 20cm.

**Q.4: ****Find the perimeter of a rectangle whose length is 9 cm and width is 16 cm.**

**Solution:**

Given,

Length = 9 cm

Width = 16 cm

Perimeter of Rectangle= 2(Length + Width)

= 2(9 + 16) cm

= 2 x 25 cm

Therefore, the perimeter of a rectangle= 50 cm

**Q.5: Find the perimeter of a rectangle whose length and width is 20 cm and 9 cm, respectively.**

**Solution:**

Given,

Length = 20 cm

Width = 9 cm

Perimeter of Rectangle = 2(Length + Width)

= 2(20 +9) cm

= 2 x 29 cm

Therefore, the perimeter of a rectangle = 58 cm

To learn about more geometrical concepts, learn with BYJU’S and also download its app to get personalised learning videos.

**Example 1**: Ann wants to add some lace as decoration to the borders of her bedsheet. The bedsheet is in the shape of a rectangle. The length of the bedsheet is 120 inches and the width is 85 inches. How much lace will she need to put around it?

Solution:

Given, length = 120 inches; width = 85 inches. We know that the perimeter of a rectangle is equal to twice the sum of its length and width. Hence, Perimeter of a rectangle = 2(l+w). Applying the values of length and width in this formula, we have Perimeter = 2(l + w) = 2(120 + 85)= 2 × 205 = 410 inches.

Therefore, Ann will need 410 inches of lace.

**Example 2: **Your favorite chocolate bar is made up of equal-sized squares with each side measuring 1 inch. Calculate the perimeter of the rectangular choco bar.

**Solution:**

We know that each little square has all its sides equal to 1 inch. If we count and add the sides of the squares along the length of the bar, we get 6 inches. The sides of squares along the width of the bar add up to 2 inches. Therefore, the length of the bar is 6 inches and the width of the bar is 2 inches. Applying this in the perimeter formula we have:

Perimeter = 2(l+w)= 2 (6+2) = 2×8 = 16 inches

Therefore, the perimeter is 16 inches.

**Perimeter of a Rectangle Sample Questions**

Here are a few sample questions going over area of a rectangle.

Question #1:

Which formula is used to calculate the perimeter of a rectangle?

Perimeter=4+(length+width)

Perimeter=^{(length × width)}/_{2}

Perimeter=(length+width)×4

Perimeter=(length+width)×2**Answer:**

A rectangle has two equal lengths and two equal widths. In order to find the perimeter, or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length. Perimeter=(length+width)×2 is the formula for perimeter.

**Question #2:**

Calculate the perimeter of the given rectangle.

22 feet

44 feet

86.5 feet

108.75 feet

**Answer:**

We can calculate the perimeter of the rectangle by using the formula Perimeter=(length+width)×2. We can see that the length is 14.5 feet and the width is 7.5 feet so our formula becomes Perimeter=(14.5+7.5)×2 which simplifies to 44. The perimeter of the rectangle is 44 feet.

**Question #3:**

Determine the perimeter of the rectangle if its area is 64 m^{2} and its length is 16 m.

40 meters

45 meters

30 meters

38 meters

**Answer:**

In order to determine the perimeter of the rectangle, we first need to determine the width (w). The area of a rectangle is calculated by multiplying length×width, so we can use the following equation to solve for our missing value (w).

Area = l × w

64 m^{2}=16 × w

Divide both sides by 16 to solve for w.

w = 4, or 4 m

Now that we know the length and the width, we can use the formula Perimeter=(length+width)×2 in order to solve for the perimeter. When we plug in 16 m for our length and 4 m for our width, we have the following: Perimeter=(16m+4m)×2, which simplifies to 40 m. The perimeter of the rectangle is 40 meters.

**Question #4:**

The side lengths of a rectangular sandbox in Sunnyland Park are 15 feet and 8.5 feet. Determine the perimeter of the sandbox.

47 feet

42 feet

46.5 feet

49.5 feet

**Answer:**

We can calculate the perimeter of the sandbox by using the formula Perimeter=(length+width)×2. We know that the length is 15 feet and the width is 8.5 feet so we can plug these values into the formula in order to solve for Perimeter. Our formula now becomes Perimeter=(15+8.5)×2 which simplifies to 47, or 47 feet.

**Question #5:**

Gloria is designing a garden for her backyard. She knows that she wants to have 24 square feet in the garden, but she is flexible as far as what the dimensions are. She wants to put a fence around the garden, but fencing (per foot) can be quite expensive so she wants to compare options. Option A is to build a garden with dimensions of 8 feet by 3 feet. Option B is to build a garden with dimensions of 6 feet by 4 feet. Which option will require less fencing and therefore a lower cost?

Option A is less expensive

Option B is less expensive

**Answer:**

Option A has a length of 8 feet and a width of 3 feet. The perimeter of this garden is 22 feet.

Option B has a length of 6 feet and a width of 4 feet. The perimeter of this garden is 20 feet.

Option B requires less fencing; therefore, it is the less expensive option.

### Practice Questions

- Find the perimeter of a given rectangle which has length = 15 cm and width = 20 cm.
- What is the length of the rectangular field which has a perimeter of 100 cm and width of 25 cm?

## Frequently Asked Questions on Perimeter of Rectangle

### What is the area and perimeter of a rectangle?

The area of a rectangle can be defined as the region that the rectangle covers in a two-dimensional space. The area of a rectangle can also be defined as the number of square units it takes to completely fill the rectangle.

The perimeter of a rectangle is defined as the total distance around the outside of a rectangle. In simple words, a rectangle’s perimeter is the total boundary of it.

### How to find the perimeter of a rectangle?

To get the perimeter of a rectangle, add all the sides of it. There are 4 sides of a rectangle whose sum will give its perimeter.

We can calculate the perimeter of a rectangle in three simple steps. The three steps listed below are helpful to find the perimeter.

**Step 1:**To calculate the perimeter of a rectangle, the length, and width should be known.**Step 2:**The respective values of length and width are substituted in the formula.**Step 3:**After solving the equation, the value of the perimeter is calculated.

The formula used to calculate the perimeter of a rectangle is:

**Perimeter of a rectangle** = 2(l + w).

Let us look at two different cases of the perimeter of a rectangle formula.

- If the perimeter and the length of a rectangle are known, the width can be calculated using the formula: Width = P/2 – l, where l = length of the rectangle; and w = width of the rectangle,
- In the same way, if the perimeter and the width are known, the length can be calculated using the formula: Length(L) = P/2 – w. Where P = perimeter of the rectangle; and w = width of the rectangle.

### What is the formula for the perimeter of a rectangle?

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.

Or, P = 2(length + breadth)

### What is Perimeter of Rectangle in Math?

The perimeter of a rectangle in math is a measurement value that is defined as the total length or distance around the boundaries of a rectangular shape. The perimeter of a rectangle is measure in meters, feet, inches, or yards.

### What is the Perimeter of a Rectangle Formulas?

Formulas used to calculate the perimeter of a rectangle are:

- Perimeter of a rectangle = 2(l + w).
- If the perimeter and the length of a rectangle are known, the width = P/2 – l, where l = length, w = width,
- If the perimeter and the width are known, Length(L) = P/2 – w. Where P = perimeter of the rectangle; and w = width.

### How to Find the Area of a Rectangle in Terms of Perimeter of a Rectangle?

If the perimeter of a rectangle is given, we also need to know either the length or the width to find its area. For example, if the length and perimeter is given, the width can be calculated. Perimeter = 2(length + width), width = (Perimeter/2) – length. Now, the required values to find the area of a rectangle are known. So, these values can be substituted in the formula: Area = length × width.

### How to Find Perimeter of Rectangle with Diagonal?

If the diagonal of a rectangle is given then by using the following perimeter of rectangle formula we can determine the perimeter of a rectangle.

Perimeter of rectangle with diagonal = 2l + 2 \(\sqrt{d^{2} – l^{2}}\)Units.

### What are the Units of Perimeter of a Rectangle?

The units of the perimeter of a rectangle are the same as its length which is usually given in meters, centimeters, inches, or yards. The perimeter is equal to the boundary of the rectangle which can be calculated with the formula: Perimeter = Length + Length + Width + Width = 2(Length + Width).

### Is the Area and Perimeter of a Rectangle the Same?

No, the area and the perimeter of a rectangle are different. The area of a rectangle is the total space covered by it and it is expressed in square units, while the perimeter is the total measure of its boundary and it is expressed in linear units.

### What is the Perimeter of a Rectangle with the Area Given?

If the area of a rectangle is given, we need to know either the length or the width of the rectangle to find its perimeter. For example, if the length and the area is known, the width can be calculated: Area = length × width. So, width = Area /length. Now, all the required values to calculate the perimeter of a rectangle are known. So, these values can be substituted in the formula: Perimeter = 2(length + width).

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