Chapter 20: Mensuration Exercise 20.2

Question: 1

Find the perimeter of the rectangle whose lengths and breadths are given below:

(i) 7 cm, 5 cm

(ii) 5 cm, 4 cm

(iii) 7.5 cm, 4.5 cm

Solution:

(i) Perimeter of a rectangle = 2 × (Length + Breadth)

Since, Length = 7 cm, Breadth = 5 cm

Therefore, Perimeter = 2 × (7 + 5) = 2 × (12) = 24 cm

(ii) Perimeter of a rectangle = 2 × (Length + Breadth)

Since, Length = 5 cm, Breadth = 4 cm

Therefore, Perimeter = 2 × (5 + 4) = 2 × (9) = 18 cm

(iii) Perimeter of a rectangle = 2 × (Length + Breadth)

Since, Length = 7.5 cm, Breadth = 4.5 cm

Therefore, Perimeter = 2 × (7.5 + 4.5) = 2 × (12) = 24 cm

Question: 2

Find the perimeter of the squares whose sides are given below:

(i) 10 cm

(ii) 5 m

(iii) 115.5 cm

Solution:

Perimeter of a square = 4 × (Length of one side)

(i) Length of one side = 10 cm

Perimeter = 4 × 10 = 40 cm

(ii) Length of one side = 5 m

Perimeter = 4 × 5 = 20 m

(iii) Length of one side = 115.5 cm

Perimeter = 4 × 115.5 = 462 cm

Question: 3

Find the side of the square whose perimeter is:

(i) 16 m

(ii) 40 cm

(iii) 22 cm

Solution:

Side of a square = Perimeter 4

(i) Perimeter = 16 m

Side of this square = 16/4 = 4 m

(ii) Perimeter = 40 cm

Side of this square = 40/4 = 10 cm

(iii) Perimeter = 22 cm

Side of this square = 22/4 = 5. 5 cm

Question: 4

Find the breadth of the rectangle whose perimeter is 360 cm and whose length is

(i) 116 cm

(ii) 140 cm

(iii) 102 cm

Solution:

Perimeter of a rectangle = 2 (Length + Breadth)

Therefore, Breadth of the rectangle = Perimeter/2 – Length

(i) Perimeter = 360 cm

Length = 116 cm

Breadth = 360/2 – 116

= 180 – 116 = 64 cm

(ii) Perimeter = 360 cm

Length = 140 cm

Breadth = 360/2 – 140

= 180 -140 = 40 cm

(iii) Perimeter = 360 cm

Length = 10/2 cm

Breadth = 360/2 – 102 = 180 – 102 = 78 cm

Question: 5

A rectangular piece of lawn is 55 m wide and 98 m long. Find the length of the fence around it.

Solution:

Length of the lawn = 98 m

Breadth of the lawn = 55 m

Length of the fence around the lawn = Perimeter of the lawn = 2 × (Length + Breadth)

Perimeter of the lawn = 2 × (98 + 55) m = 2 × (153) = 306 m

Thus, the length of the fence around the lawn = 306 m

Question: 6

The side of a square field is 65m. What is the length of the fence required all around it?

Solution:

Side of the square field = 65 m

Length of the fence around the square field = Perimeter of the square field = 4 × (Side of the square)

Perimeter of the square field = 4 × 65 = 260 m

Thus, the length of the fence around the square filed = 260 m

Question: 7

Two sides of a triangle are 15 cm and 20 cm. The perimeter of the triangles is 50 cm. What is the third side?

Solution:

Given: Perimeter = 50 cm

Length of the first side = 15 cm

Length of the second side = 20 cm

We have to find the length of the third side.

Perimeter of a triangle = Sum of all three sides of the triangle

Length of the third side = (Perimeter of the triangle) – (Sum of the length of the other two sides)

= 50 – (15 + 20)

= 50 – 35 = 15 cm

Question: 8

A wire of length 20 m is to be folded in the form of a rectangle. How many rectangles can be formed by folding the wire if the sides are positive integers in metres?

Solution:

It is given that a wire of length 20 m is to be folded in the form of a rectangle;

Therefore, we have: Perimeter of the rectangle = 20 m

⟹ 2 (Length + Breadth) = 20 m

⟹ (Length + Breadth) = 20/2 = 10 m

Since, length and breadth are positive integers in metres, therefore, the possible dimensions are: (1m, 9m), (2m, 8m), (3m, 7m), (4m, 6m) and (5m, 5m)

Thus, five rectangles can be formed with the given wire.

Question: 9

A square piece of land has each side equal to 100 m. If 3 layers of metal wire have to be used to fence it, what is the length of the wire?

Solution:

Side of the square field = 100 m

Wire required to fence the square field = Perimeter of the square field = 4 × Side of the square field Perimeter = 4 × 100 = 400 m

This perimeter is the length of wire required to fence one layer.

Therefore, the length of wire required to fence three layers = 3 × 400 m = 1200 m

Question: 10

Shikha runs around a square of side 75 m. Priya runs around a rectangle with length 60 m and breadth 45 m. Who covers the smaller distance?

Solution:

Shikha and Priya, while running around the square and rectangular field respectively, actually cover a distance equal to the perimeters of these fields.

Distance covered by Shikha = Perimeter of the square = 4 × 75 m = 300 m

Similarly, distance covered by Priya = Perimeter of the rectangle = 2 × (60 + 45)

= 2 × 105 = 210 m

Thus, it is evident that the distance covered by Priya is less than that covered by Shikha.

Question: 11

The dimensions of a photographs are 30 cm X 20 cm. What length of wooden frame is needed to frame the picture?

Solution:

Dimensions of the photograph = 30 cm x 20 cm

So, the required length of wooden frame = Perimeter of the photograph

= 2 (Length + Breadth)

= 2 × (30 + 20) cm = 2 × 50 cm

= 100 cm