document.write( "Question 238957: An open rectangular gutter is made by turning up the sides of a piece of metal 20in. wide. The area of the cross-section of the gutter is 50in^2. Find the depth of the gutter. \n" ); document.write( "

Algebra.Com's Answer #175560 by Earlsdon(6294) $\"\"$ $\"About$

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Let d = the depth of the gutter and w = its width.
\n" ); document.write( "The area of the cross-section can be expressed as:
\n" ); document.write( " $\"A+=+d%2Aw\"$ and this is given as 50 sq.in.
\n" ); document.write( "The cross-section however consists of only three sides, d+d+w and the sum of these dimensions is given as 20 in.
\n" ); document.write( "So we can write the following:
\n" ); document.write( "1) $\"2d%2Bw+=+20\"$ and
\n" ); document.write( "2) $\"d%2Aw+=+50\"$
\n" ); document.write( "Rewrite equation 1) as $\"w+=+20-2d\"$ and substitute into equation 2).
\n" ); document.write( "2a) $\"d%2820-2d%29+=+50\"$ Simplify and solve for d, the depth.
\n" ); document.write( "2b) $\"20d-2d%5E2+=+50\"$ Rewrite as a quadratic equation in standard form.
\n" ); document.write( "2c) $\"2d%5E2-20d%2B50+=+0\"$ Solve by factoring.
\n" ); document.write( "2d) $\"%282d-10%29%28d-5%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( "2e) $\"2d-10+=+0\"$ or $\"d-5+=+0\"$ which means that...
\n" ); document.write( " $\"highlight%28d+=+5%29\"$
\n" ); document.write( "The depth of the gutter is 5 inches. \n" ); document.write( "

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