document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #548106 by josgarithmetic(39617) $\"\"$ $\"About$

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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
\n" ); document.write( " $\"%28x-2a%29%28y-2a%29a=528\"$ ;\r
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\n" ); document.write( "\n" ); document.write( "\"Length is twice its width\" for rectangle's dimensions:
\n" ); document.write( "If x is length, and y is width, then x=2y, and $\"%282y-2a%29%28y-2a%29a=528\"$
\n" ); document.write( " $\"2y%5E2-2ay-4ay%2B4a%5E2-528=0\"$
\n" ); document.write( " $\"2y%5E2-6ay%2B4a%5E2-528=0\"$
\n" ); document.write( " $\"highlight%28y%5E2-3ay%2B2a%5E2-264=0%29\"$
\n" ); document.write( "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. \r
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\n" ); document.write( "\n" ); document.write( "Once that is done, you can substitute the a=3 and evaluate that more specific case. \n" ); document.write( "

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