document.write( "Question 942634: A piece of sheet metal, w = 20 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 48 square inches, find the depth of the gutter. \n" ); document.write( "
Algebra.Com's Answer #574704 by ankor@dixie-net.com(22740)\"\" \"About 
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A piece of sheet metal, w = 20 inches wide, is bent to form the gutter shown in the illustration.
\n" ); document.write( " If the cross-sectional area is 48 square inches, find the depth of the gutter.
\n" ); document.write( ":
\n" ); document.write( "let d = the debth of the gutter
\n" ); document.write( "let x =the width of the gutter
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\n" ); document.write( "Sort of like this, the width is x
\n" ); document.write( " d|__|d
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\n" ); document.write( "We know: 2d + x = 20
\n" ); document.write( "therefore:
\n" ); document.write( "x = (20-2d)
\n" ); document.write( ":
\n" ); document.write( " and
\n" ); document.write( "x*d = 48, the cross-sectional area
\n" ); document.write( "Replace x with (20-2d)
\n" ); document.write( "d(20-2d) = 48
\n" ); document.write( "A quadratic is equation is formed
\n" ); document.write( "-2d^2 + 20d - 48 = 0
\n" ); document.write( "Simplify, divide by -2
\n" ); document.write( "d^2 - 10d + 24
\n" ); document.write( "Factors to
\n" ); document.write( "(d-6)(d-4) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "d = 6
\n" ); document.write( "d = 4
\n" ); document.write( "Find x
\n" ); document.write( "when d = 6 inches
\n" ); document.write( "x = 20 - 2(6)
\n" ); document.write( "x = 8 inches wide (6*8=48 square inches)
\n" ); document.write( ":
\n" ); document.write( "when d = 4 inches
\n" ); document.write( "x = 20 - 2(4)
\n" ); document.write( "x = 12 inches wide (4*12=48 square inches) \n" ); document.write( "
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