The dimensions of a rectangular box are int he ratio of `2:3:4` and the difference between the cost of covering it with sheet of paper at the rates of `R s .8` and `R s .9.50p e rm^2` is `R s .1248.` Find the dimensions of the box.

Explanation

Let common multiple of `2:3:4` be `x`
`Breadth = 2x`
` Length = 3x`
`Height = 4x`
Surface area = `2(2x xx3x + 3x xx4x + 4x xx2x)`
`2(6x^2+12x^2+8x^2) `
`52x^2 cm^2`
According the question
`Rs[9.5(52x^2)-8(52x^2)]`
` Rs. 1248`
`1.5(52x^2) = 1248`
` x^2 = 1248/(1.5xx52)`
`x^2=16`
`x = sqrt16 = 4`
` Breadth = 2(4) = 8cm`
Length `= 3(4) = 12cm`
` Height = 4(4) = 16cm`