A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in³. The length is 4 inches greater than twice the width. What is the width of the box?

Solution:

Given, volume of rectangular prism = 2,720 in³

Height of prism = 17 in

Let, length be L and width be W

Length = 4 + 2 width

L = 4 + 2W

We have to find the width of the box.

Volume = length × width × height

2720 = L × W × 17

2720 = (4 + 2W) × W × 17

(4 + 2W) × W = 2720 / 17

(4 + 2W) × W = 160

4W + 2W² = 160

2W² + 4W - 160 = 0

Dividing by 2

W² + 2W - 80 = 0

On solving,

W² + 10W - 8W - 80 = 0

W(W + 10) - 8(W + 10) = 0

(W - 8)(W + 10) = 0

W - 8 = 0

W = 8

W + 10 = 0

W = -10

The value cant be negative

Therefore, the width of the box is 8 in.

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A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in³. The length is 4 inches greater than twice the width. What is the width of the box?

Summary:

A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in³. The length is 4 inches greater than twice the width. The width of the box is 8 in.