Question

The length, breadth, and height of a rectangular solid are in the ratio 5: 4: 2. If the total surface area is 1216 cm², find the length, the breadth, and the height of the solid.

Answer 1

The rectangular solid is a cuboid.

Let the length of the cuboid = 5a, breadth = 4a, and height = 2a

Total surface area of a cuboid of length l, breadth b and height h = 2(l × b + b × h + l × h)

Given,

Total surface area of the cuboid = 1216 cm²
⇒ 2(5a × 4a + 4a × 2a + 2a × 5a) = 1216 cm²
⇒ 76a² = 1216
⇒ a = 4.

Hence, the length of the cuboid = 5a = 20 cm, breadth = 4a = 16 cm, height = 2a = 8 cm.