document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239613>Question 239613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many scalene triangles have a perimeter of less than 13? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175823 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=175823\">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( "The way you ask the question, an infinite number.  However, if you restrict the measures of the sides to the integers, then there is a small finite set of three integer sets such that no set of three has a duplicated integer and the sum of each set is 13.\r<BR>\n" );
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document.write( "For example, 1, 2, and 10 is one such set\r<BR>\n" );
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document.write( "1, 3, 9\r<BR>\n" );
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document.write( "and so on.  Then\r<BR>\n" );
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document.write( "2, 3, 8\r<BR>\n" );
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document.write( "2, 4, ...\r<BR>\n" );
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document.write( "You get the idea.  Just be careful not to duplicate any numbers in a set of 3 because if you duplicate, then you no longer have a scalene triangle, you have an isosceles triangle.  For example, 3, 5, 5 -- no good.\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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