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?

• A. 248 m²
• B. 48 m²
• C. 84 m²
• D. 56 m²
• E. 260 m²

Hint:

Surface area of walls = Perimeter of base × Height.

Answer 1

The Correct Option is C

Step 1: Defining Variables:
Let breadth = \(b\) meters, length = \(b + 2\) meters.
Original area = \(b(b + 2)\).
New length = \((b + 2) + 4 = b + 6\), new breadth = \(b - 2\).
New area = \((b + 6)(b - 2)\).

Step 2: Equating Areas:
\[ b(b + 2) = (b + 6)(b - 2) \]
\[ b^2 + 2b = b^2 + 4b - 12 \]
\[ 2b = 4b - 12 \]
\[ 12 = 2b \]
\[ b = 6 \]
So, breadth = 6 m, length = 8 m.

Step 3: Surface Area of Walls:
Surface area of four walls = \(2 \times \text{height} \times (\text{length} + \text{breadth})\)
\[ = 2 \times 3 \times (8 + 6) = 6 \times 14 = 84 \text{ m}^2 \]