SOLUTION: A rectangular piece of cardboard has a total length that measures 6 inches more than its total width. A 2-inch by 2-inch square is cut out of each corner, and the remaining sides a

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Question 296244: A rectangular piece of cardboard has a total length that measures 6 inches more than its total width. A 2-inch by 2-inch square is cut out of each corner, and the remaining sides are turned up at the dotted lines and their edges taped together to make a box with no top. The volume of the box is 110 cubic inches. What were the dimensions of the original piece of cardboard?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If L and W are the length and width, respectively, of the original piece of cardboard, and the cut-out corners are 2X2 inches, then the volume (V) of the newly-formed open top box with a height (h) of 2 inches can be expressed as:
V+=+%28L-4%29%2A%28W-4%29%2Ah Substitute L+=+W%2B6%29
V+=+%28%28W%2B6%29-4%29%2A%28W-4%29%2A2 and the volume of this box is given as V+=+110cu.in., so we can write:
110+=+%28W%2B2%29%2A%28W-4%29%2A2 Simplify and solve for W.
110+=+2%28W%5E2-2W-8%29 Divide both sides by 2.
55+=+W%5E2-2W-8 Subtract 55 from both sides.
W%5E2-2W-63+=+0 Solve by factoring.
%28W%2B7%29%28W-9%29+=+0 so that...
W+=+-7 or W+=+9 Discard the negative solution as the width W is a positive quantity.
highlight%28W+=+9%29inches. and...
L+=+W%2B6
highlight%28L+=+15%29inches.