document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134281>Question 1134281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a perimeter of 34cm. One of its diagonals is 13cm. Find its sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751628 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let l be length and w be width, we know that<BR>\n" );
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document.write( "2l +2w = 34<BR>\n" );
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document.write( "1) l +w = 17<BR>\n" );
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document.write( "By Pythagorean Theorem, we know that<BR>\n" );
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document.write( "2) l^2 +w^2 = 13^2 = 169<BR>\n" );
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document.write( "Solve equation 1 for l and substitute for l in equation 2<BR>\n" );
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document.write( "l = 17-w<BR>\n" );
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document.write( "(17-w)^2 +w^2 = 169<BR>\n" );
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document.write( "289 -34w +w^2 +w^2 = 169<BR>\n" );
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document.write( "2w^2 -34w +120 = 0<BR>\n" );
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document.write( "divide both sides of = by 2<BR>\n" );
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document.write( "w^2 -17w +60 = 0<BR>\n" );
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document.write( "(w-12) * (w-5) = 0<BR>\n" );
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document.write( "w = 12, w = 5<BR>\n" );
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document.write( "We have two solutions for the rectangle<BR>\n" );
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document.write( "1) length = 12 cm and width = 5 cm<BR>\n" );
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document.write( "2) length = 5 cm and width = 12 cm<BR>\n" );
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document.write( "Note usually the length is greater than the width for a rectangle<BR>\n" );
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