document.write( "Question 102304: 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 16 square inches, find the depth of the gutter. (there are two answers a smaller value and a larger value)The width is represented by w-2x and the depth is x \n" ); document.write( "
Algebra.Com's Answer #74383 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. If the cross-sectional area is 16 square inches, find the depth of the gutter. (there are two answers a smaller value and a larger value)The width is represented by w-2x and the depth is x
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\n" ); document.write( "Assume the illustration:
\n" ); document.write( "|__|x; is the cross-sectional area of 16 sq in and the sides & bottom = 18\"
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\n" ); document.write( "x = sides dimension
\n" ); document.write( "y = bottom dimension
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\n" ); document.write( "2x + y = 18
\n" ); document.write( "y = (18-2x)
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\n" ); document.write( "Area:
\n" ); document.write( "x * y = 16
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\n" ); document.write( "Substitute (18-2x) for y:
\n" ); document.write( "x*(18-2x) = 16
\n" ); document.write( "-2x^2 + 18x - 16 = 0; a quadratic equation
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\n" ); document.write( "Simplify, divide equation by -2
\n" ); document.write( "x^2 - 9x + 8 = 0
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\n" ); document.write( "Factors to:
\n" ); document.write( "(x - 8) * (x - 1) = 0
\n" ); document.write( "x = +8
\n" ); document.write( "and
\n" ); document.write( "x = +1
\n" ); document.write( ":
\n" ); document.write( "The gutter can be:
\n" ); document.write( "8\" high and 2\" wide
\n" ); document.write( "or
\n" ); document.write( "1\" high and 16\" wide
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