Question

The dimensions of a rectangular box are in the ratio of 2: 3: 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m² is Rs 1248. Find the dimensions of the box.

Answer 1

Given details are,

Ratio of dimensions of rectangular box = 2:3:4

Let length of box be ‘2x’ m

Let breadth of box be ‘3x’ m

Let height of box be ‘4x’ m

Area of sheet of paper required for covering it = total surface area of cuboid

= 2 (lb+bh+hl)

= 2 (2x×3x + 3x×4x + 4x×2x)

= 2 (6x² + 12x² + 8x²)

= 2 (26x²)

= 52 x² m²

Cost for covering with sheet of paper at the rate of Rs 9.50 /m² = 52x² × 9.50

= Rs 494x²

Cost for covering with sheet of paper at the rate of Rs 8 /m² = 52x² × 8

= Rs 416x²

Given, the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m² is Rs 1248

494x² – 416x² = 12448

78x² = 1248

x² = 1248/78

= 16

x = √16

= 4

∴ Length of box = 2x = 2×4 = 8m

Breadth of box = 3x = 3×4 = 12m

Height of box = 4x = 4×4 = 16m