document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=602117>Question 602117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I know the polygon to get the number of diagonals I can use the formula     n(n-3)/2  where n=the number of sides of the polygon.  How can I find the polygon when I know the number of diagonals that can be drawn inside?  ex.  Which polygon has 20 diagonals that can be drawn inside?  Is there a formula for this question? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380125 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=380125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let d = number of diagonals\r<BR>\n" );
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document.write( "The formula to find the number of diagonals 'd' is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28n%28n-3%29%29%2F2 ALIGN=MIDDLE  ALT=\"d=%28n%28n-3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve this for n to find the number of sides given the number of diagonals\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28n%28n-3%29%29%2F2 ALIGN=MIDDLE  ALT=\"d=%28n%28n-3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d=n%28n-3%29 ALIGN=MIDDLE  ALT=\"2d=n%28n-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d=n%5E2-3n ALIGN=MIDDLE  ALT=\"2d=n%5E2-3n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=n%5E2-3n-2d ALIGN=MIDDLE  ALT=\"0=n%5E2-3n-2d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2-3n-2d=0 ALIGN=MIDDLE  ALT=\"n%5E2-3n-2d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the quadratic formula to solve for 'n'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"n+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%281%29%28-2d%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"n+=+%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%281%29%28-2d%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%283%2B-sqrt%289%2B8d%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"n+=+%283%2B-sqrt%289%2B8d%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%283%2Bsqrt%289%2B8d%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"n+=+%283%2Bsqrt%289%2B8d%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%283-sqrt%289%2B8d%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"n+=+%283-sqrt%289%2B8d%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So things are a bit uglier, but now you have a formula for 'n' given the number of diagonals 'd'. </SPAN>\n" );
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