SOLUTION: A large plywood box has a volume of 1008 ft^3. Its length is 16 ft greater than its height, and its width is 9 ft less than its height. What are the dimensions of the box?

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Question 703974: A large plywood box has a volume of 1008 ft^3. Its length is 16 ft greater than its height, and its width is 9 ft less than its height. What are the dimensions of the box?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Length and width both are described in relation to height. Height is the first variable to solve for.

Volume, v=1008=L%2AW%2AH=%2816%2BH%29%28H-9%29H
1008=%28H%2B16%29%28H-9%29H

This will work into H%5E3%2B7H%5E2-144H-1008=0, so you'll look for roots of this equation. You'll want to check for positive values for H. There are plenty of different rational roots to check, but your best choice will be for H at 12. One of the binomial factors for the cubic expression should be H-12. Also note, the roots to look for can't be too terribly big, since your box is based on dimensions not too far from about 16 or 20; so don't try to look for roots too far above this size.