volume of rectangular prism

Question

A rectangular prism with volume 3200

mm^3 has a rectangular base whose width

is 4/5 of its length. If the height of the

prism is 5 times its width, what is the

height of the prism?

Answer 1

volume = length * width * height

w = width

w = 4/5 length

length = 5/4 width = 5/4 w

height = 5w

5w * 5/4w * w = 3200

25/4 w^3 = 3200

w^3 = 512

w = 8

height = 5*w = 5* 8 = 40

length = (5 /4)w = 5/4 (8) = 10

verification

volume = 8 * 40 * 10 = 3200