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
