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.