SOLUTION: A rectangular sheet of metal is 6 inches longer than it is wide. A box is to be made by cutting out 3 inch squares at each corner and folding up the sides. If the box has a volume

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Question 1157082: A rectangular sheet of metal is 6 inches longer than it is wide. A box is to be made by cutting out 3 inch squares at each corner and folding up the sides. If the box has a volume of 336 inches cubed, what were the original dimensions of the sheet metal?
Answer by ikleyn(52781) About Me  (Show Source):
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The original dimensions were  W inches wide and  (W + 6) inches long.


After making the box, dimensions of its base are  (W-2*3) wide and ((W+6)-2*3) long.


The volume is 3*(W-6)*W, and the equation to find W is


    3W*(W-6) = 336,   or

    W^2 - 6W - 112 = 0.

    (W-14)*(W+8) = 0

     W = 14.


ANSWER.  The original dimensions were  14 by 20 inches.

Solved.