SOLUTION: A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a

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Question 903510: A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 528 in^3, when a = 3?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are the original rectangle dimensions; the area for the bottom after cutting the a inch squares is (x-2a)(y-2a). The volume of the box will be
%28x-2a%29%28y-2a%29a=528;

"Length is twice its width" for rectangle's dimensions:
If x is length, and y is width, then x=2y, and %282y-2a%29%28y-2a%29a=528
2y%5E2-2ay-4ay%2B4a%5E2-528=0
2y%5E2-6ay%2B4a%5E2-528=0
highlight%28y%5E2-3ay%2B2a%5E2-264=0%29
Continue solving for y using the general solution to a quadratic formula, and use the y result to get x=2y. That will be for any "a" in general.

Once that is done, you can substitute the a=3 and evaluate that more specific case.