document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086341>Question 1086341</A>: <I><SPAN STYLE=\"word-break: break-all;\">  An n-sided polygon has <BR>\n" );
document.write( "(n(n - 3))/2 diagonals. a How many sides has a polygon with 665 diagonals? b Why can’t a polygon have 406 diagonals?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700518 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Number of diagonals = d = (n/2)(n-3) -> n^2 - 3n - 2d = 0<BR>\n" );
document.write( "a) Solve for n, when d = 665<BR>\n" );
document.write( "n^2 - 3n - 1330 = 0<BR>\n" );
document.write( "This can be factored as (n-38)(n+35) = 0<BR>\n" );
document.write( "We take the positive solution, n = 38<BR>\n" );
document.write( "For d = 406, we have the equation n^2 - 3n - 812 = 0<BR>\n" );
document.write( "This does not give an integer solution for n.  Thus no polygon can have 406 diagonals. </SPAN>\n" );
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