document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443094>Question 443094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the hypotenuse of a right triangle measures 29 cm. one leg is 1 cm shorter than the other. what are the lenghts of the legs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305631 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+29 ALIGN=MIDDLE  ALT=\"c+=+29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we know that one of the legs is 1 less than the other. Let's choose a to be 1 less than b.\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b-1 ALIGN=MIDDLE  ALT=\"a+=+b-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-1%29%5E2+%2B+b%5E2+=+29%5E2 ALIGN=MIDDLE  ALT=\"%28b-1%29%5E2+%2B+b%5E2+=+29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-1%29%2A%28b-1%29+%2B+b%5E2+=+29%5E2 ALIGN=MIDDLE  ALT=\"%28b-1%29%2A%28b-1%29+%2B+b%5E2+=+29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-b+-b+%2B1++%2Bb%5E2+=+29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+-b+-b+%2B1++%2Bb%5E2+=+29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-2b+%2B+1+%2Bb%5E2+=+29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+-2b+%2B+1+%2Bb%5E2+=+29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2+-2b+%2B+1+=+841 ALIGN=MIDDLE  ALT=\"2b%5E2+-2b+%2B+1+=+841\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2+-2b+-840 ALIGN=MIDDLE  ALT=\"2b%5E2+-2b+-840\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28b%5E2+-b+-420%29 ALIGN=MIDDLE  ALT=\"2%2A%28b%5E2+-b+-420%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28b%2B20%29%28b-21%29 ALIGN=MIDDLE  ALT=\"2%28b%2B20%29%28b-21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So b=-20 or b=21<BR>\n" );
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document.write( "But it does not make sense to have a negative length, so the one that makes LOGICAL sense is b =21\r<BR>\n" );
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document.write( "If b =21, then a=20 since a = b-1.\r<BR>\n" );
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document.write( "So we have (20,21,29) is our triangle.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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