document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949469>Question 949469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a right triangle the length of the longer leg is 2 centimeters more than twice the length of the shorter leg. the length of the hypotenuse is 8 centimeters more than the length of the shorter leg. find in centimeters the length of the 3 sides 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 #579655 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=579655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "let  the hypotenuse be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,the longer leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we know that in a right triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1\r<BR>\n" );
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document.write( "given:<BR>\n" );
document.write( "in a right triangle the length of the longer leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cm ALIGN=MIDDLE  ALT=\"2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than twice the length of the shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we have\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2b%2B2cm ALIGN=MIDDLE  ALT=\"a=2b%2B2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the length of the hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8cm ALIGN=MIDDLE  ALT=\"8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than the length of the shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=b%2B8cm ALIGN=MIDDLE  ALT=\"c=b%2B8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   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%2B8cm%29%5E2=%282b%2B2cm%29%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28b%2B8cm%29%5E2=%282b%2B2cm%29%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28b%5E2%29%2B16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2%2Bcross%28b%5E2%29 ALIGN=MIDDLE  ALT=\"cross%28b%5E2%29%2B16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2%2Bcross%28b%5E2%29\"   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=16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2 ALIGN=MIDDLE  ALT=\"16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4b%5E2-16b%2Acm%2B8b%2Acm%2B4cm%5E2-64cm%5E2 ALIGN=MIDDLE  ALT=\"0=4b%5E2-16b%2Acm%2B8b%2Acm%2B4cm%5E2-64cm%5E2\"   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=4b%5E2-8b%2Acm-60cm%5E2=0 ALIGN=MIDDLE  ALT=\"4b%5E2-8b%2Acm-60cm%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify, divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=b%5E2-2b%2Acm-15cm%5E2=0 ALIGN=MIDDLE  ALT=\"b%5E2-2b%2Acm-15cm%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor completely, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2b%2Acm ALIGN=MIDDLE  ALT=\"-2b%2Acm\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5b%2Acm%2B3b%2Acm ALIGN=MIDDLE  ALT=\"-5b%2Acm%2B3b%2Acm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-5b%2Acm%2B3b%2Acm-15cm%5E2=0 ALIGN=MIDDLE  ALT=\"b%5E2-5b%2Acm%2B3b%2Acm-15cm%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2-5b%2Acm%29%2B%283b%2Acm-15cm%5E2%29=0 ALIGN=MIDDLE  ALT=\"%28b%5E2-5b%2Acm%29%2B%283b%2Acm-15cm%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%28b-5cm%29%2B3cm%28b-5cm%29=0 ALIGN=MIDDLE  ALT=\"b%28b-5cm%29%2B3cm%28b-5cm%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-5cm%29%28b%2B3cm%29+=+0 ALIGN=MIDDLE  ALT=\"%28b-5cm%29%28b%2B3cm%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-5cm%29+=+0 ALIGN=MIDDLE  ALT=\"%28b-5cm%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5cm ALIGN=MIDDLE  ALT=\"b=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B3cm%29+=+0 ALIGN=MIDDLE  ALT=\"%28b%2B3cm%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3cm ALIGN=MIDDLE  ALT=\"b=-3cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >..-> disregard negative value because we are looking for the length\r<BR>\n" );
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document.write( "so, our solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=5cm%29 ALIGN=MIDDLE  ALT=\"highlight%28b=5cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2b%2B2cm ALIGN=MIDDLE  ALT=\"a=2b%2B2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2%2A5cm%2B2cm ALIGN=MIDDLE  ALT=\"a=2%2A5cm%2B2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=12cm%29 ALIGN=MIDDLE  ALT=\"highlight%28a=12cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=b%2B8cm ALIGN=MIDDLE  ALT=\"c=b%2B8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5cm%2B8cm ALIGN=MIDDLE  ALT=\"c=5cm%2B8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=13cm%29 ALIGN=MIDDLE  ALT=\"highlight%28c=13cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "check if Pythagoras theorem works:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813cm%29%5E2=%2812cm%29%5E2%2B%285cm%29%5E2 ALIGN=MIDDLE  ALT=\"%2813cm%29%5E2=%2812cm%29%5E2%2B%285cm%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=169cm%5E2=144cm%5E2%2B25cm%5E2 ALIGN=MIDDLE  ALT=\"169cm%5E2=144cm%5E2%2B25cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169cm%5E2=169cm%5E2 ALIGN=MIDDLE  ALT=\"169cm%5E2=169cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >............true; so, these are sides of right angle triangle\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );