document.write( "Question 706353: A piece of sheet metal, w = 16 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 24 square inches, find the depth of the gutter. \n" ); document.write( "

Algebra.Com's Answer #435116 by josgarithmetic(39617) $\"\"$ $\"About$

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No picture is shown in your question on the site, but one would imagine the sides are folded bent upward at x from the each side, leaving 16-2x for a bottom width for this gutter. You then wish to have the cross section of 16-2x by 1x area be 24 SQUARE inches. \r
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\n" ); document.write( "\n" ); document.write( " $\"%2816-2x%29x=24\"$
\n" ); document.write( "(8-x)x=12
\n" ); document.write( "8x-x^2=12
\n" ); document.write( "-x^2+8x=12
\n" ); document.write( "x^2-8x=-12
\n" ); document.write( " $\"x%5E2-8x%2B12=0\"$
\n" ); document.write( "Factorable to
\n" ); document.write( " $\"%28x-6%29%28x-2%29=0\"$ \n" ); document.write( "

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