**Perimeter of Rectangle Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on perimeter of rectangle.

Before look at the worksheet, if you would like to learn the stuff perimeter of rectangle,

**Problem 1 :**

The length and width of a rectangle are 16 cm and 12 cm respectively. Find its perimeter.

**Problem 2 :**

If the perimeter of a rectangle is 50 cm and its length is 15 cm, then find its width.

**Problem 3 :**

The area of the rectangle is 150 square inches. If the length is twice the width, then find its perimeter.

**Problem 4 :**

The length of a rectangle is 3 ft and one of the diagonal measures √13 ft. Find its perimeter.

**Problem 5 :**

The length of a rectangle is 3 yards more than its width and its perimeter is 18 yards. Find its length and width.

**Problem 6 :**

The length and width of a rectangle are in the ratio 3 : 4 and its perimeter is 98 inches. Find its length and width.

**Problem 7 :**

Mr. John would like to fence his rectangular shaped garden. The length of the garden is 13 ft and width is 10 ft. If the cost of fencing is $8 per feet, then find the total cost of fencing for the entire garden.

**Problem 8 :**

The length of a rectangle is 70 cm and width is 30 cm. If the length is increased by 10% and width is by 20%, then find the percentage increase in perimeter.

**Problem 1 :**

The length and width of a rectangle are 16 cm and 12 cm respectively. Find its perimeter.

**Solution:**

Formula for perimeter of a rectangle :

= 2(l + w)^{ }

Substitute 16 for l and 12 for w.

= 2(16 + 12)

= 2(28)

= 56

So, the perimeter of the rectangle is 56 cm.

**Problem 2 :**

If the perimeter of a rectangle is 50 cm and its length is 15 cm, then find its width.

**Solution:**

Perimeter of the rectangle = 50 cm

2(l + w) = 50

Divide each side by 2.

l + w = 25

Substitute 15 for l.

15 + w = 25

Subtract 15 from each side.

w = 10

So, the width of the rectangle is 10 cm.

**Problem 3 :**

The area of the rectangle is 150 square inches. If the length is twice the width, then find its perimeter.

**Solution:**

Let x be the width of the rectangle.

Then, the length of the rectangle is 2x.

Area of the rectangle = 150 in^{2}

l ⋅ w = 150

x ⋅ 2x = 150

2x^{2} = 150

Divide each side by 2.

x^{2} = 75

Find positive square root on both sides.

√x^{2 } = √75

x = √(5 ⋅ 5 ⋅ 3)

x = 5√3

Therefore, the width of the rectangle is 5√3 in.

Then, the length of the rectangle is

= 2 ⋅ width

= 2 ⋅ 5√3

= 10√3 in

Formula for perimeter of a rectangle :

= 2(l + w)

Substitute 10√3 for l and 5√3 for w.

= 2(10√3 + 5√3)

= 2(15√3)

= 30√3

So, the perimeter of the rectangle is 30√3 in.

**Problem 4 :**

The length of a rectangle is 3 ft and one of the diagonal measures √13 ft. Find its perimeter.

**Solution:**

To find the perimeter of a rectangle, we have to know its length and width. Length is given in the question, that is 3 ft. So, find its width.

Draw a sketch.

In the figure shown above, consider the right triangle ABC.

By Pythagorean Theorem, we have

AB^{2} + BC^{2} = AC^{2}

Substitute.

AB^{2} + 3^{2} = (√13)^{2}

Simplify and solve for AB.

AB^{2} + 9 = 13

Subtract 9 from each side.

AB^{2} = 4

Find positive square root on both sides.

√AB^{2} = √4

AB = 2

Therefore, the width of the rectangle is 2 ft.

Formula for perimeter of a rectangle.

= 2(l + w)

Substitute 3 for l and 2 for w.

= 2(3 + 2)

= 2(5)

= 10

So, the perimeter of the rectangle is 10 ft.

**Problem 5 :**

The length of a rectangle is 3 yards more than its width and its perimeter is 18 yards. Find its length and width.

**Solution:**

Let x be the width of the rectangle.

Then, the length of the rectangle is (x + 3) yards.

Perimeter of the rectangle = 18 yards

2(l + w) = 18

Divide each side by 2.

l + w = 9

Substitute (x + 3) for l and x for w.

(x + 3) + x = 9

x + 3 + x = 9

2x + 3 = 9

Subtract 3 from each side.

2x = 6

Divide each side by 2.

x = 3

x + 3 = 6

So, the length and width of the rectangle are 6 yards and 3 yards respectively.

**Problem 6 :**

The length and width of a rectangle are in the ratio 3 : 4 and its perimeter is 98 inches. Find its length and width.

**Solution:**

**From the ratio 3 : 4, let the length and width of the rectangle be 3x and 4x respectively.**

**Perimeter of the rectangle = 98 inches**

2(l + w) = 98

Divide each side by 2.

l + w = 49

Substitute 3x for l and 4x for w.

3x + 4x = 49

7x = 49

Divide each side by 7.

x = 7

Length = 3x = 3(7) = 21 in

Width = 4x = 4(7) = 28 in

So, the length and width of the rectangle are 21 inches and 28 inches respectively.

**Problem 7 :**

Mr. John would like to fence his rectangular shaped garden. The length of the garden is 13 ft and width is 10 ft. If the cost of fencing is $8 per feet, then find the total cost of fencing for the entire garden.

**Solution:**

To find the total cost of fencing the entire garden, we have to know the perimeter of the garden. So, find the perimeter.

Formula for perimeter of a rectangle :

= 2(l + w)

Substitute 13 for l and 10 for w.

= 2(13 + 10)

= 2(23)

= 46 ft

Therefore, the perimeter of the garden is 46 ft.

The cost of fencing is $8 per feet.

Then, the total cost of fencing 46 ft :

= 46 ⋅ 8

= 368

So, the total cost of fencing for the entire garden is $368.

**Problem 8 :**

The length of a rectangle is 70 cm and width is 30 cm. If the
length is increased by 10% and width is by 20%, then find the percentage increase in perimeter.

**Solution:**

**Before increase in length and width :**

Formula for perimeter of a rectangle :

= 2(l + w)

Substitute 70 for l and 30 for w.

= 2(70 + 30)

= 2(100)

= 200 cm

Therefore, the perimeter of the rectangle is 200 cm.

**After increase in length and width :**

Length = (100 + 10)% of 70 = 1.1 ⋅ 70 = 77 cm

Width = (100 + 20)% of 30 = 1.2 ⋅ 30 = 36 cm

Formula for perimeter of a rectangle :

= 2(l + w)

Substitute 77 for l and 36 for w.

= 2(77 + 36)

= 2(113)

= 226 cm

Therefore, the perimeter of the rectangle is 226 cm.

**Percentage increase in perimeter :**

Increase in perimeter = 226 - 200

Increase in perimeter = 26 cm

Percentage increase in perimeter = (26 / 200) ⋅ 100 %

Percentage increase in perimeter = 13%

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