Question

A gift bag shaped like a rectangular prism has a volume of 1152 cubic inches. The dimensions of the gift bag in terms of its width are shown. The height is greater than the width.

What are the dimensions of the gift bag?

length: in.
width: in.
height: in.

Answer 1

• Given below.

Explanation:

Gift bag is shaped in a rectangular prism.

rectangular volume: length * width * height

( 2w + 4 ) ( w ) ( 18 - w ) = 1152

( 2w² + 4w ) ( 18 - w ) = 1152

-2w³+32w² +72w = 1152

-2w³+32w² +72w - 1152 = 0

`-2\left(w-16\right)\left(w+6\right)\left(w-6\right)=0`

w = 16 , -6 , 6

w = 16 , 6

• length = ( 2w + 4 ) = 36 inch , 16 inch

• width = ( w ) = 16 inch , 6 inch

• height = ( 18 - w ) = 2 inch , 12 inch