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?

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(39617) (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,

This will work into , 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.
RELATED QUESTIONS
A large plywood box has a volume of 240 ft^3. Its length is 16 ft greater than its... (answered by ptaylor)

A large plywood box has a volume of 180 ft ( square). Its length is 9 ft greater than its (answered by Nate)

large plywood box has a volume of 768 ft3. Its length is 16 ft greater than its height,... (answered by ankor@dixie-net.com)

A large plywood box has a volume of 12 ft3. Its length is 4 ft greater than its height,... (answered by DrBeeee)

A large plywood box has a volume of 240 ft3. Its length is 16 ft greater than its height, (answered by stanbon)

Please help me with this word problem: A large plywood box has a volume of 72 ft3. Its... (answered by ankor@dixie-net.com)

A large plywood box has a volume of 1440 ft3. Its length is 18 ft greater than its... (answered by harpazo)

I need help with the following word problem: A large plywood box has a volume of 324 ft3. (answered by ankor@dixie-net.com,nerdybill)

A rectangular solid has a volume of 180 ft cubed. Its length is 6 ft and its width is 5... (answered by jim_thompson5910)