document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239265>Question 239265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> RAIN-GUTTER DESIGN:  An open rectangle 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.  Can you please help me find the depth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175696 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> RAIN-GUTTER DESIGN: An open rectangle gutter is made by turning up the sides of a piece of metal 20 in. wide.<BR>\n" );
document.write( " The area of the cross- section of the gutter is 50 in^2. <BR>\n" );
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document.write( "Let d = the depth<BR>\n" );
document.write( "Let w = the width of the gutter<BR>\n" );
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document.write( "d|__|d would be a picture of the end of it, the horizontal line is the width (w)<BR>\n" );
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document.write( "the piece of metal is 20\" wide, therefore: <BR>\n" );
document.write( "2d + w = 20<BR>\n" );
document.write( "w = (20-2d)<BR>\n" );
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document.write( "The area = depth * width<BR>\n" );
document.write( "d * w = 50<BR>\n" );
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document.write( "Replace w with (20-2d)<BR>\n" );
document.write( "d(20-2d) = 50<BR>\n" );
document.write( "-2d^2 + 20d - 50 = 0; our old friend, the quadratic equation!<BR>\n" );
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document.write( "Simplify and change the signs, divide by -2<BR>\n" );
document.write( "d^2 - 10d + 25 = 0<BR>\n" );
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document.write( "Factors easily to:<BR>\n" );
document.write( "(d - 5)(d - 5) = 0<BR>\n" );
document.write( "d = 5 inches is the depth<BR>\n" );
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document.write( "Lets see if this is true<BR>\n" );
document.write( "w = 20 - 2d<BR>\n" );
document.write( "w = 20 - 10<BR>\n" );
document.write( "w = 10 inches is the width<BR>\n" );
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document.write( "Check the area 5 * 10 = 50<BR>\n" );
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document.write( "Did this make sense to you? Did I explain it well enough for you to understand? </SPAN>\n" );
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