Question

The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2 meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.

Accepted Answer

D. Let the breadth of the room be $x$ meters. Then, length = $x + 2$ meters. Initial Area = $x(x + 2) = x^2 + 2x$. New length = $x + 6$ meters, New breadth = $x - 2$ meters. New Area = $(x + 6)(x - 2) = x^2 + 4x - 12$. Since area remains the same: $$x^2 + 2x = x^2 + 4x - 12$$ $$2x = 12 \implies x = 6$$ So breadth = 6 m, length = 8 m, height = 3 m. Surface area of 4 walls = $2(l + b)h = 2(8 + 6) 	imes 3 = 2 	imes 14 	imes 3 = 84	ext{ m}^2$.

Surface area of room walls

Explanation

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