document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074446>Question 1074446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right angled triangle with hypotenuse 20cm. A square 6cm placed in the right angle of the triangle. The hypothenuse touches the top right corner of the square. <BR>\n" );
document.write( "What is length of other two sides?\r<BR>\n" );
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document.write( "I started usi g similar triangles and called base (x+6) and height (y+6) getting <BR>\n" );
document.write( "y=36/x.  Then use Pythagoras. But can't simplify the complicated algebra I get after that. \r<BR>\n" );
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document.write( "Can anyone help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689248 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=se3.png\">.<BR>\n" );
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document.write( "By Pythagoras,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%5E2%2B%28y%2B6%29%5E2=20%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%5E2%2B%28y%2B6%29%5E2=20%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By similar triangles,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F6=%28y%2B6%29%2F%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y%2F6=%28y%2B6%29%2F%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28y%2B6%29=y%28x%2B6%29 ALIGN=MIDDLE  ALT=\"6%28y%2B6%29=y%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29=%286%28y%2B6%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28x%2B6%29=%286%28y%2B6%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%5E2=%2836%28y%2B6%29%5E2%29%2Fy%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%5E2=%2836%28y%2B6%29%5E2%29%2Fy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836%28y%2B6%29%5E2%29%2Fy%5E2%2B%28y%2B6%29%5E2=400 ALIGN=MIDDLE  ALT=\"%2836%28y%2B6%29%5E2%29%2Fy%5E2%2B%28y%2B6%29%5E2=400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%28y%2B6%29%5E2%2By%5E2%28y%2B6%29%5E2=400y%5E2 ALIGN=MIDDLE  ALT=\"36%28y%2B6%29%5E2%2By%5E2%28y%2B6%29%5E2=400y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%28y%5E2%2B12y%2B36%29%2B%28y%5E4%2B12y%5E3%2B36y%5E2%29=400y%5E2 ALIGN=MIDDLE  ALT=\"36%28y%5E2%2B12y%2B36%29%2B%28y%5E4%2B12y%5E3%2B36y%5E2%29=400y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836y%5E2%2B432y%2B1296%29%2B%28y%5E4%2B12y%5E3%2B36y%5E2%29=400y%5E2 ALIGN=MIDDLE  ALT=\"%2836y%5E2%2B432y%2B1296%29%2B%28y%5E4%2B12y%5E3%2B36y%5E2%29=400y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4%2B12y%5E3%2B72y%5E2%2B432y%2B1296=400y%5E2 ALIGN=MIDDLE  ALT=\"y%5E4%2B12y%5E3%2B72y%5E2%2B432y%2B1296=400y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4%2B12y%5E3-328y%5E2%2B432y%2B1296=0 ALIGN=MIDDLE  ALT=\"y%5E4%2B12y%5E3-328y%5E2%2B432y%2B1296=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=f9.JPG\">.<BR>\n" );
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document.write( "Graphing finds two positive solutions,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.04 ALIGN=MIDDLE  ALT=\"y=3.04\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=11.84 ALIGN=MIDDLE  ALT=\"y=11.84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with corresponding x values,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29=%286%28y%2B6%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28x%2B6%29=%286%28y%2B6%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11.84 ALIGN=MIDDLE  ALT=\"x=11.84\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.04 ALIGN=MIDDLE  ALT=\"x=3.04\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then the lengths of the other sides are,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6=17.84 ALIGN=MIDDLE  ALT=\"x%2B6=17.84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B6=9.04 ALIGN=MIDDLE  ALT=\"y%2B6=9.04\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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