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.

Respuesta :

Answer:

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

Step-by-step 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:

[tex]10H^2+30H=1800[/tex]

Dividing by 10:

[tex]H^2+3H=180[/tex]

Rearranging:

[tex]H^2+3H-180=0[/tex]

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

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