SOLUTION: The box has a volume of 16 cubic feet. The width should be 2 feet less than the height. The length should be 4 feet greater than the height. Find the dimensions of the box.

Question 415899: The box has a volume of 16 cubic feet. The width should be 2 feet less than the height. The length should be 4 feet greater than the height. Find the dimensions of the box.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
he box has a volume of 16 cubic feet.
L * W * H = 16
:
The width should be 2 feet less than the height.
W = H-2
:
The length should be 4 feet greater than the height.
L = H+4
:
Replace L and W in the 1st equation
(H+4) * (H-2) * H = 16
FOIL
(H^2 - 2H + 4H - 8) * H = 16
:
H(H^2 + 2H - 8) = 16
:
H^3 + 2H^2 - 8H - 16 = 0
No integer solution for this, plot it on your trusty graphing calc
y = x^3 + 2x^2 - 8x - 16

Find the positive solution using the 0 feature
x = 2.8284
so we have
L = 6.8284
W = 0.8284
H = 2.8284
:
You can confirm this by finding the vol using these values

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