Question 706433
A large plywood box has a volume of 324 ft3. Its length is 12 ft greater than its height, and its width is 3 ft less than its height.
 What are the dimensions of the box?
:
That's the way you do it, it would be 
(h+12)*(h-3)* h = 324
FOIL
(h^2 - 3h + 12h - 36) * h = 324
(h^2 + 9h - 36) * h = 324
h^3 + 9h^2 - 36h - 324 = 0
We can group factor this
h^2(h+9) - 36(h+9)
Factor out (h+9)
(h+9)(h^2-36) = 0
we are only interested in the positive solution
h^2 = 36
h = 6 ft is the height
then
L = 18, W = 3 ft
:
Check: 18 * 3 * 6 = 324