document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305638>Question 305638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 25. If the altitude from the right angle to the hypotenuse is 12, what is the length of the longest segment it forms on the hypotenuse?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218831 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=218831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+250%2C+-0%2C+30%2C+-0%2C+15%2C%0D%0Aline%280%2C0%2C9%2C12%29%2C%0D%0Aline%289%2C12%2C25%2C0%29%2C%0D%0Aline%289%2C12%2C9%2C0%29%2C%0D%0Aline%280%2C0%2C25%2C0%29%2C%0D%0Alocate%289%2C6%2C12%29%2C%0D%0Alocate%284%2C8%2Cb%29%2C%0D%0Alocate%2816%2C8%2Ca%29%2C%0D%0Alocate%284%2C1%2Cx%29%2C%0D%0Alocate%2814%2C1%2C25-x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And with a tip of the hat to Mr. Pythagoras we begin:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25^2\ =\ a^2\ +\ b^2\">\r<BR>\n" );
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document.write( "which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^2\ =\ 25^2\ -\ b^2\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2\ =\ 12^2\ +\ x^2\">\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 \ \ \ \ \ \ \ \ \ \ a^2\ =\ 12^2\ +\ (25\,-\,x)^2\">\r<BR>\n" );
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document.write( "Which expands to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^2\ =\ 12^2\ +\ 25^2\ -\ 50x\ +\ x^2\">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25^2\ -\ b^2\ =\ 12^2\ +\ 25^2\ -\ 50x\ +\ x^2\">\r<BR>\n" );
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document.write( "and simplifying\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -\ b^2\ =\ 12^2\ -\ 50x\ +\ x^2\">\r<BR>\n" );
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document.write( "but since\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2\ =\ 12^2\ +\ x^2\">\r<BR>\n" );
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document.write( "we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2\ =\ 25x\">\r<BR>\n" );
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document.write( "But then we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25x\ =\ 12^2\ +\ x^2\">\r<BR>\n" );
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document.write( "and in standard form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 25x\ +\ 144 =0\">\r<BR>\n" );
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document.write( "which factors to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 9)(x\ -\ 16)\ =\ 0\">\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 9\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 16\">\r<BR>\n" );
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document.write( "which is the situation if the diagram was turned over.  Since the question asks for the longer of the two segments, the answer is 16.\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" );
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