Question

The volume of a box is 1800 cubic Inches. If the length of the box is 10 inches and its width is 3 inches more than its height, find the width and

height of the box.

Answer 1

The width of the box is 15 inches and its height is 12 inches

Explanation:

Equations

The volume of a box of width W, height H, and length L is given by:

V=W*L*H

We know

L=10 inches

W=H+3

V=1800 cubic meters

Substituting:

1800=(H+3)*10*H

Operating and swapping sides:

`10H^2+30H=1800`

Dividing by 10:

`H^2+3H=180`

Rearranging:

`H^2+3H-180=0`

Factoring:

(H-12)(H+15)=0

The only positive and valid result is:

H=12 inches

Thus,

W=H+3=12+3=15 inches

The width of the box is 15 inches and its height is 12 inches