A rectangular prism has a volume of 384 cm. The width is twice the height and the length is three times the height. What are the dimensions of the prism?

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the dimensions of this rectangular prism such that the formula for the volume yields,

l*w*h = V

Since the length is 3 times the height, it is l = 3x, height = x and width = 2x. Then for the formula yields,

(3x)(2x)(x) = 384

6x³ = 384............Then divide 6 such that

x³ = 64............Then we take the cube root of both sides such that

x = 4 cm

Then the length is 12 cm, the height is 4 cm and the width is 8 cm.

I hope this helped!