SOLUTION: A box with an open top is constrcuted by cutting a-inch suares from the corners of a rectangular sheet of tin whose lenght is twice its width. What size sheet will produce a box ha

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Question 714474: A box with an open top is constrcuted by cutting a-inch suares from the corners of a rectangular sheet of tin whose lenght is twice its width. What size sheet will produce a box having a volume of 60 cubic inches, when a = 2.
Answer by josgarithmetic(39618) About Me  (Show Source):
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The sheet in one direction is w long, and in the other direction is 2w long. A 2 inch by 2 inch corner is being removed and the flaps be turned, folded to form the open box. That means, the base of this open box will be w-2%2A2 by 2w-2%2A2.

The volume, given as 60 cubic inches, is the area of the base multiplied by how high this box is, and is given as 2 inches high, since a=2.
Volume, highlight%2860=%28w-2%2A2%29%282w-2%2A2%29%2A2%29
60=2%2A2%28w-4%29%28w-2%29
15=%28w-4%29%28w-2%29
15=w%5E2-6w%2B8
w%5E2-6w-7=0
highlight%28%28w-7%29%28w%2B1%29+=0%29

The only value that makes sense is w=7 inches.
The sheet is 7 inches by 14 inches.