The dimensions of a rectangular box are in the ratio 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 `m^2` is Rs. 1248. Find the dimensions of the box.

Explanation

Ratio in the dimensions of a cuboidal box`=2:3:4`
Let length `l=4x`
Breadth `b=3x`
Height `h=2x`
Total surface area`=2(lb+bh+hl)`
`=2(4xtimes3x+3xtimes2x+2xtimes4x)cm^2`
`=2(12x^2+6x^2+8x^2)`
`=2times26x^2=52x^2`
Cost of covering it with sheet of paper`=Rs.(52x^2times9.50-52x^2times8)`
Difference in the cost of covering it with sheet of paper`=Rs. 1248`
According to the condition:
`1248=(52x^2times9.50-52x^2times8)`
`1248=(494x^2-416x^2)`
`1248=78x^2`
`x^2=1248/78=16`
`x=sqrt16=4`
`therefore` The dimensions of the box are:
`l=4times4=16 m`
`b=3times4=12 m`
`h=2×4=8 m`