Rectangular problem .

[Md.Nazrul Islam]

The interior of a rectangular cartoon is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height is 3:2:2.In terms of 'x' what is the height of the cartoon in feet .

[Anurag@Gurome]

The interior of a rectangular cartoon is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height is 3:2:2.In terms of 'x' what is the height of the cartoon in feet .

Let us assume that the length = 3n, width = 2n and height = 2n
Then volume = length * width * height = 3n * 2n * 2n = 12(n^3) = x cubic ft
Solving 12(n^3) = x, we get
n^3 = x/12
n = (x/12)^(1/3)

Therefore, height of the carton = 2 * n = [spoiler]2 * (x/12)^(1/3)[/spoiler]

[gmatmath]

Given the ratio of length to width to height = 3:2:2.
so, Let the length'l' = 3k, width'w' = 2k and height'h' = 2k
Volume = lxwxh
x = 3k*2k*2k
x = 12k^3
==> k = (x/12)^(1/3)
so, height 'h' = 2k = 2[(x/12)^(1/3)
or h = two times the cuberoot of (x/12)