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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

By the quadratic formula,

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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