document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8491>Question 8491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many sides a convex polygan have  if it has 35 distinct diagnals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4701 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Assume it is a convex polygon with n sides\r<BR>\n" );
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document.write( " For each vertex v,  there are n-3 possible diagonals passing through v.<BR>\n" );
document.write( " (except the two adjacent vertices & v itself)<BR>\n" );
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document.write( " Since a diagonal (a line segment was counted twice from the two end<BR>\n" );
document.write( " vertices), totally there are n(n-3)/2 = 35 diagonals.\r<BR>\n" );
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document.write( " Solve n(n-3)= 70, or n^2 - 3n - 70 = 0<BR>\n" );
document.write( " Factoring (n-10)(n+7) = 0.<BR>\n" );
document.write( " So n = 10 or n = -7(Illegal)\r<BR>\n" );
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document.write( " Answer : n = 10\r<BR>\n" );
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document.write( " Forget another terribly wrong answer,\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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