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

llm

Answered on Thu May 12 2022

V=l*w*h

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

6x^3 = 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.