document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621160>Question 621160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the length of the shorter side of a right triagle if the longer leg is 24 meters, and the hypotenuse is 6 more than twice the shorter leg.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390596 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the length of the shorter side of a right triagle if the longer leg is 24 meters, and the hypotenuse is 6 more than twice the shorter leg.<BR>\n" );
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document.write( "Let x = length of shorter leg<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2x+6 = hypotenuse<BR>\n" );
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document.write( "applying the Pythagorean theorem:<BR>\n" );
document.write( "x^2 + 24^2 = (2x+6)^2<BR>\n" );
document.write( "x^2 + 576 = (2x+6)(2x+6)<BR>\n" );
document.write( "x^2 + 576 = 4x^2+24x+36<BR>\n" );
document.write( "576 = 3x^2+24x+36<BR>\n" );
document.write( "0 = 3x^2+24x-540<BR>\n" );
document.write( "dividing both sides by 3:<BR>\n" );
document.write( "0 = x^2+8x-180<BR>\n" );
document.write( "0 = (x+18)(x-10)<BR>\n" );
document.write( "x = {-18,10}<BR>\n" );
document.write( "throw out the negative solution leaving:<BR>\n" );
document.write( "x = 10 meters (shorter side)<BR>\n" );
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