Question

A square carpet when placed in a room leaves a strip 1 m wide uncarpeted along one pair of opposite walls and a strip 2 m wide along the other two walls.

If the area uncarpeted is 62 sq m, what is the length of the carpet ?

(a) 10 m

(b) 9 m

(c) 8 m

(d) 7 m

Answer 1

Correct option is (b) 9 m

Let the side of the carpet be x m.

Then as per the figure, the length of the sides of the room = x + 4; x + 2

Given, area of the uncarpeted area = 62 sq m

⇒ (x + 4) (x + 2) − x² = 6²

⇒ x² + 4x + 2x + 8 − x² = 6²

⇒ 6x + 8 = 62

⇒ 6x = 54

⇒ x = 9

Hence, the length of the carpet = 9 m.