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# Advanced Math/Dimensions - Metal Used for Box

Question
A rectangular sheet of metal is used to construct a box.  The box is formed by removing squares from the corners and bending up the remaining sides.  Determine dimensions of metal used.

Volume of box - 168 in.^3
Size of squares removed - 1.5"

Thanks.

You haven't specified the shape of the box, so I'll assume it has a square base.
The sheet of metal is x inches by x inches.
The box will be x-3 inches long by x-3 inches wide by 1.5 inches high.
volume = (x-3)(x-3)1.5 = 168
1.5x² - 9x + 13.5 = 168
1.5x² - 9x - 154.5 = 0

x = [9 ± √(9² – 4·1.5(-154.5))] / [2·1.5]
= [9 ± √1008] / 3
= [9 ± 12√7] / 3
= 3 ± 4√7
3-4√7 is an extraneous solution, so x = 3+4√7 ≅ 13.583 inches
The sheet of metal is 13.583 inches by 13.583 inches.

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