document.write( "Question 400594: A piece of sheet metal, w = 18 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 28 square inches, find the depth of the gutter.\r
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Algebra.Com's Answer #283588 by ankor@dixie-net.com(22740)\"\" \"About 
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A piece of sheet metal, w = 18 inches wide, is bent to form the gutter shown in the illustration.
\n" ); document.write( " If the cross-sectional area is 28 square inches, find the depth of the gutter.
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\n" ); document.write( "Let d = the debth of the gutter
\n" ); document.write( "then
\n" ); document.write( "(18-2d) = the width of the gutter
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\n" ); document.write( " d|__|d
\n" ); document.write( "The bottom dimension is (18-2d)
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\n" ); document.write( "The cross sectional area:
\n" ); document.write( "d(18-2d) = 28
\n" ); document.write( "-2d^2 + 18d = 28
\n" ); document.write( "A quadratic equation
\n" ); document.write( "-2d^2 + 18d - 28 = 0
\n" ); document.write( "Multiply by -1, to make it easier to factor
\n" ); document.write( "2d^2 - 18d + 28 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(2d - 4)(d - 7) =
\n" ); document.write( "Two solutions
\n" ); document.write( "2d = 4
\n" ); document.write( "d = 2
\n" ); document.write( "and
\n" ); document.write( "d = 7 inches is probably the reasonable value for the depth of gutter
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\n" ); document.write( "Check:
\n" ); document.write( "the width of the gutter 18 - 2(7) = 4 inches
\n" ); document.write( "Check the area: 7 * 4 = 28 sq/inches
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