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.

Given,

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

Let dimensions are = 2x ,3x , 4x

So, total surface area of box = 2(6x²+12x²+8x²) = 52 x²

Let, c₁ = cost of covering at rate Rs. 8 per m²

C₁ = 8×52x²

Let c₂ = cost of covering at rate Rs.9.50 per m²

C₂ = 9.50× 52x²

= C₂ – C₁ = 1248 (given)

= 52x²×9.50 – 52x²×8 = 1248

= 52x² =

= x² =

= x = 4

Hence dimensions of box are = 2x = 2×4 = 8 cm

= 3x = 3×4 = 12 cm

=4x= 4×4 = 16cm