The length of a rectangular prism is four times the height of the prism and one-third the width of the prism. If the volume of the prism is 384 in3, what is the width of the prism?

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The length of a rectangular prism is four times the height of the prism and one-third the width of the prism. If the volume of the prism is 384 in3, what is the width of the prism?

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Answer: 24

Explanation:

If the height of the prism is h, then the length of the prism is four times that, 4h. The length is one-third of the width, so the width is three times the length: 12h.

The volume of the prism is equal to its length multiplied by its width multiplied by its height:

h × 4h × 12h

48h 3 = 384

h 3 = 8

h = 2

The height of the prism is 2 in, the length of the prism is 2  in × 4 = 8 in, and the width of the prism is 8 in × 3 = 24 in.