13, Theratioofdimensionsofacuboidalboxis2:3:4OX 1S 2:3:The difference between the cost of wrapping thebox at the rate of74 per square meter andper square meter is R 416. Find the dimensions ofthe cuboidal box.[Board Term II, Set-RQTZFBW, 2016]

13, Theratioofdimensionsofacuboidalboxis2:3:4OX 1S 2:3:The difference

1.	13, Theratioofdimensionsofacuboidalboxis2:3:4OX 1S 2:3:The difference between the cost of wrapping thebox at the rate of74 per square meter andper square meter is R 416. Find the dimensions ofthe cuboidal box.[Board Term II, Set-RQTZFBW, 2016]
Answer» Since the ratio of a cuboidal box are 2:3:4.So suppose the dimensions of cuboid box are 2x, 3x and 4x respectively.So total surface area of box =2(2x3x+3x4x+2x4x)=52x^2Cost of wrapping the box at rate of Rs.4.50 per square metre =52x^24.50=234x^2And cost of wrapping the box at rate of Rs. 4 per square metre =5x^24=208x^2Now according to the question we have;234x^2-208x^2=41626x^2=416x^2=16x=4So dimensions of cuboidal box are(24),(34),(44)Therefore dimensions of box are 8 m, 12 m, and 16 m.