The dimensions of a cuboid are in the ratio 5 : 3 : 2. If total surface area of the cuboid is 558 cm², then find the length of edges of the cuboid.

Let

Length of cuboid = l = 5x

Breadth of cuboid = b = 3x

Height of cuboid = h = 2x

Such that the ratio is 5:3:2 as mentioned in question where x is any positive number

Total surface area of cuboid = 558 cm²

Total surface area of cuboid = 2 × (lb + bh + hl)

⇒ 558 = 2 × [(5x)(3x) + (3x)(2x) + (2x)(5x)]

⇒ = 15x² + 6x² + 10x²

⇒ 279 = 31x²

⇒ x² =

⇒ x² = 9

⇒ x = ± 3

x is length therefore x cannot be negative therefore x = 3

therefore,

length of cuboid = 5x = 5 × 3 = 15 cm

breadth of cuboid = 3x = 3 × 3 = 9 cm

height of cuboid = 2x = 2 × 3 = 6 cm

length of edges of cuboid are 15 cm, 9 cm and 6 cm