document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263025>Question 263025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain and solve. Thank you.<BR>\n" );
document.write( "A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional area of 13 square inches. Show that there are 2 different solutions to the problem. Round to the nearest tenth of an inch.<BR>\n" );
document.write( "x(20+2x)= 13. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193779 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional area of 13 square inches. Show that there are 2 different solutions to the problem. Round to the nearest tenth of an inch.<BR>\n" );
document.write( "x(20+2x)= 13.<BR>\n" );
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document.write( "The cross-section is a slice thru the gutter from top thru the bottom.<BR>\n" );
document.write( "The shape is a \"U\".<BR>\n" );
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document.write( "If height = base = x inches you get x^2 = 13 and x = sqrt(13)<BR>\n" );
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document.write( "If base is x then height is (20-x)/2:<BR>\n" );
document.write( "x(20-x)/2 = 13<BR>\n" );
document.write( "20x - x^2 = 26<BR>\n" );
document.write( "x^2 -20x + 26 = 0<BR>\n" );
document.write( "x = [20 +- sqrt(400 - 4*1*26)]/2<BR>\n" );
document.write( "x = [20 +- sqrt(296)]/2<BR>\n" );
document.write( "x = [20 + 17.2]/2 = 37.2/2 = 18.6\"<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "x = [20 - 17.2]/2 = 1.4\"<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So base could be 18.6 and height be (1.4/2) = 0.7\"<BR>\n" );
document.write( "Or base could be 1.4\" and height be (18.6/2) = 9.3\"<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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