SOLUTION: large plywood box has a volume of 768 ft3. Its length is 16 ft greater than its height, and its width is 4 ft less than its height. What are the dimensions of the box
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Question 706395: large plywood box has a volume of 768 ft3. Its length is 16 ft greater than its height, and its width is 4 ft less than its height. What are the dimensions of the box
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
large plywood box has a volume of 768 ft3.
L * W * h = 768
:
Its length is 16 ft greater than its height,
L = (h+16)
:
and its width is 4 ft less than its height.
W = (h-4)
:
(h+16)*(h-4)* h = 768
FOIL
(h^2 - 4h + 16h - 64) * h = 768
(h^2 + 12h - 64) * h = 768
h^3 + 12h^2 - 64h - 768 = 0
We can group factor this
h^2(h+12) - 64(h+12)
Factor out (h+12)
(h+12)(h^2-64) = 0
we are only interested in the positive solution
h^2 = 64
h = 8 ft is the height
then
L = 24, W = 4 ft
:
Check: 24 * 4 * 8 = 768
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