document.write( "Question 109246This question is from textbook Introductory Algebra
\n" ); document.write( ": An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in.^2. Find the depth of the gutter. \n" ); document.write( "

Algebra.Com's Answer #79674 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in.^2. Find the depth of the gutter.
\n" ); document.write( ":
\n" ); document.write( "Let x = depth of gutter
\n" ); document.write( ":
\n" ); document.write( "The cross section would look sort of like this:
\n" ); document.write( "x|__|x
\n" ); document.write( ":
\n" ); document.write( "The bottom = (20 - 2x)
\n" ); document.write( ":
\n" ); document.write( "Area:
\n" ); document.write( "x(20-2x)= 50
\n" ); document.write( "-2x^2 + 20x - 50 = 0
\n" ); document.write( "Divide equation by -2 to simplify
\n" ); document.write( "x^2 - 10x + 25 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(x-5)(x-5) = 0
\n" ); document.write( "x = 5 inches is depth of the gutter
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "Bottom = 20 - 2(5) = 10
\n" ); document.write( "5 * 10 = 50 sq/in as given \n" ); document.write( "

\n" );