document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276703>Question 276703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The measures of the sides of a right triangle are those of a Pythagorean triple. If the measure of the shortest side is 17, what are the measures of the other two sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201626 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=201626\">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( "PPT = Primitive Pythagorean Triple.\r<BR>\n" );
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document.write( "The shortest leg in a PPT is always odd, so we know that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2n\ +\ 1\ =\ 17\">. The other leg in a PPT is always 4 times a triangle number -- a triangle number being the sum of consecutive integers beginning at 1 and the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\">th one being given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n(n+1)}{2}\">, which multiplied by 4 is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2n(n\,+\,1)\">.  And the hypotenuse is always 1 larger than the long leg, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2n(n\,+\,1)\ +\ 1\">.\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2n\ +\ 1\ =\ 17\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 8\">.  Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 8\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2(8)((8)\,+\,1)\ =\ 16\,\cdot\,8\ =\ 144\"> for the long leg and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 144\ +\ 1\ =\ 145\"> for the hypotenuse.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{17^2\ +\ 144^2}\ =\ \sqrt{21025}\ = 145\">\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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