# The diagonal of a rectangular room is 37.5% less than the sum of

| The diagonal of a rectangular room is 37.5% less than the sum of the length, breadth and height of the room. If the diagonal of the room is 15 cm, then what is the total surface area of the room?

A. 328 cm<sup>2</sup>

B. 351 cm<sup>2</sup>

C. 335 cm<sup>2</sup>

D. 356 cm<sup>2</sup>

Please scroll down to ** see the correct answer ** and ** solution guide.**

### Right Answer is: B

#### SOLUTION

Let the length, breadth and height of the room are ‘l’, ‘b’ and ‘h’ respectively.

The length of the diagonal of the room = (l^{2} + b^{2} + h^{2})^{1/2} = 15 cm

(l^{2} + b^{2} + h^{2}) = 225 cm

The sum of the length, breadth and height of the room

l + b + h = 15 × 100/62.5 = 24 cm

Now, (l + b + h)^{2} = l^{2} + b^{2} + h^{2} + 2(lb + bh + hl)

(24)^{2} = 225 + 2(lb + bh + hl)

^{2}