Question

The length, breadth and height of a rectangular solid are in the ratio 6 : 5 : 4. If the total surface area is 5328 $c{m}^2$ , find the length, breadth and height of the solid.

Answer 1

Let length = (6x) cm, breadth = (5x) cm and height = (4x) cm.

Then, total surface area = [2(6x × 5x + 5x x 4x + 4x × 6x)] $c{m}^2$

= [2(30$x^2+20x^2+24x^2\left)\right]c{m}^2$

= (148$x^2)c{m}^2$.

148 $x^2$ = 5328
$x^2$ = 36

x = 6

Hence, length = 36 cm, breadth = 30 cm, height = 24 cm.