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.

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

Let length of box = 2x m

Breadth of box = 3x m

Height of box = 4x m

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

= 2(lb × bh × hl)

=2(6x² + 12x² + 8x²)

= 2×26x²

=52 x² m²

Cost of covering it with sheet of paper at Rs.9.50 /m²

= 52 x² × 9.50

=Rs.494 x²

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

=Rs.416 x²

= 494x²-416x²=1248 Given

= 78x²=1248

= x²=1248/78=16

= x= √16=4

So,

Length of box = 2x = 2×4 = 8 m

Breadth of box = 3x = 3×4 = 12 m

Height of box = 4x = 4×4 = 16 m