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A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah occupies an area of $22 m 2$ , find the width of the verandah.

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1 m

2 m

4 m

5 m

answer is A.

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Detailed Solution

Given a room 5 m long and 4 m wide is surrounded by a verandah.
R.D. Sharma Solutions Class 7 | Math Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) Exercise 20.2

R.D. Sharma Solutions Class 7 | Math Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) Exercise 20.2

Area of the room is,

A = l e n g t h × b r e a d t h ⇒ A = 5 m × 4 m

⇒ A = 20 m 2

The length PQ is,

P Q = 5 + x + x

P Q = 5 + 2 x m

The breadth QR is,

Q R = 4 + x + x

Q R = 4 + 2 x m

Area of veranda PQRS is,

⇒ A = (5 + 2 x) × (4 + 2 x)

⇒ A = 4 x 2 + 18 x + 20 m 2

Area of the veranda = Area of PQRS – Area of ABCD

⇒ 22 = 4 x 2 + 18 x + 20 − 20

⇒ 22 = 4 x 2 + 18 x

⇒ 11 = 2 x 2 + 9 x

⇒ 2 x 2 + 9 x − 11 = 0

Now, mid-term splitting,

⇒ 2 x 2 + 11 x − 2 x − 11 = 0

⇒ x 2 x + 11 − 1 2 x + 11 = 0

⇒ x − 1 2 x + 11 = 0

Therefore,

x − 1 = 0 ⇒ x = 1

Also,

2 x + 11 = 0 ⇒ 2 x = − 11 ⇒ x = − 11 2

As, width can’t be negative, therefore neglecting

x = − 11 2

.
Therefore, the width is 1 m.
Hence, option 1 is correct.

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