Question

The ratio of length, breadth, height of a cuboid is 5 : 3 : 2. If total surface area of the cuboid is 558 cm², find the length, breadth and height.

Answer 1

Let length (l) = 5x

breadth (b) = 3x

and height (h) = 2x

According to question

Total surface area = 2(lb + bh + hl)

or 2(5x × 3x + 3x × 2x + 2x × 5x) = 558

or 2(15x² + 6x² + 10x²) = 558

or 2 × 31x² = 558

or x² = \(\frac { 558 }{ 2\times31 }\)

or x² = 9 ⇒ x = 3

Thus, length of cuboid 

= 5x = 5 × 3 = 15 cm

Breadth = 3x = 3 × 3 

= 9 cm

and height = 2x = 2 × 3 

= 6 cm