Question

The dimensions of a cuboid are in the ratio 1:2:3 and it's total surface area is 88m find the dimensions

Answer 1

Take the dimensions as x, 2x and 3x. Then put the formula of total surface area of cuboid, that is, 2 (lb + bh + hl).
Substitute the values and get the answer.

Answer 2

Given :-
Dimensions of a cuboid are in ratio 1:2:3
Total surface area = 88m

Let
length (l) = 3x m
breadth (b) = 2x m
height (h) = 1x m

$Total \: \: surface \: \: area = 2( lb + bh + hl ) \\ \\ 88 = 2 ( lb + bh + hl ) \\ \\ 88 = 2 ( 3x \times 2x + 2x \times 1x + 1x \times 3x) \\ \\ 88 = 2 ( 6x^2 + 2x^2 + 3 {x}^{2} ) \\ \\ 88 = 2(11 {x)}^{2} \\ \\ 88 = 22 {x}^{2} \\ \\ \frac{88}{22} = {x}^{2} \\ \\ 4 = {x}^{2} \\ \\ \sqrt{4 } = x \\ \\ 2 = x$


length (l) = 3x = 3*2 = 6m
breadth (b) = 2x = 2*2 = 4m
height (h) = 1x = 1*2 = 2m