document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975491>Question 975491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of the sides of a triangle are 12cm,5cm,13cm.find the length of the perpendicular from opposite vertex to side 13cm long. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597250 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=597250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Construct your triangle and the desired perpendicular.  Note that the intersection of the perpendicular and the side measuring 13cm divides the 13cm side into two segments.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the measure of the shorter segment and then the longer segment must measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 13\ -\ x\">.  While we are at it, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> represent the height we are trying to find.  Since the height segment is perpendicular to the 13cm side of the triangle, we have divided the triangle into two right triangles, one with a hypotenuse that measures 5cm and the other with a hypotenuse that measures 12 cm.\r<BR>\n" );
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document.write( "We now invoke the magic of Mr. Pythagoras to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ h^2\ =\ 25\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (13\ -\ x)^2\ +\ h^2\ =\ 144\">\r<BR>\n" );
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document.write( "which we can expand to read\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 169\ -\ 26x\ +\ x^2\ =\ 144\">\r<BR>\n" );
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document.write( "Taking the first equation, multiplying by -1, and adding to the second equation gives:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 169\ -\ 26x\ =\ 119\">\r<BR>\n" );
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document.write( "Solving for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{25}{13}\">\r<BR>\n" );
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document.write( "Calling upon Mr. Pythagoras again we substitute into the first equation to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h^2\ =\ 25\ -\ \left(\frac{25}{13}\right)^2\">\r<BR>\n" );
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document.write( "After an abundance of arithmetic which I will let you verify for yourself, you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h\ =\ \frac{60}{13}\">\r<BR>\n" );
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document.write( "Which is the desired measurement.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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