document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5535>Question 5535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the legnths of the legs of the triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2846 by </B><A HREF=/tutors/aboutme.mpl?userid=Abbey><B>Abbey(339)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Abbey><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=2846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2Bb%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let a = shorter leg<BR>\n" );
document.write( "Let b = longer leg<BR>\n" );
document.write( "let c = hypoteneuse<BR>\n" );
document.write( "a is 14 feet shorter than b:<BR>\n" );
document.write( "a+14=b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2Bb%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can substitute a+14 in for our b, and use the hypoteneuse value of 26:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2+%2B%28a%2B14%29%5E2%29+=+26%5E2 ALIGN=MIDDLE  ALT=\"%28a%5E2+%2B%28a%2B14%29%5E2%29+=+26%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2+%2Ba%5E2%2B28a%2B196%29+=+26%5E2 ALIGN=MIDDLE  ALT=\"%28a%5E2+%2Ba%5E2%2B28a%2B196%29+=+26%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B28a%2B196=676 ALIGN=MIDDLE  ALT=\"2a%5E2%2B28a%2B196=676\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by two:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B14a%2B98=338 ALIGN=MIDDLE  ALT=\"a%5E2+%2B14a%2B98=338\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 338 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B14a-240=0 ALIGN=MIDDLE  ALT=\"a%5E2%2B14a-240=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B24%29%28a-10%29=0 ALIGN=MIDDLE  ALT=\"%28a%2B24%29%28a-10%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=-24 or a=10<BR>\n" );
document.write( "we can rule out the -24, because we are talking about a distance, which is always positive:<BR>\n" );
document.write( "so the shorter leg = 10 feet<BR>\n" );
document.write( "Put this back into the equation:\r<BR>\n" );
document.write( "\n" );
document.write( "a+14=b<BR>\n" );
document.write( "10+14=24, so the longer leg is 24 feet<BR>\n" );
document.write( "and this makes sense because <BR>\n" );
document.write( "10^2 + 24^2= 100 +576 = 676\r<BR>\n" );
document.write( "\n" );
document.write( "and 26*26 = 676<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );