document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207480>Question 1207480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a polygon of n sides has (1/2)(n)(n - 3) diagonals, how many sides will a polygon with 65 diagonals have? Is there a polygon with 80 diagonals?\r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "I understand this problem leading to this equation:\r<BR>\n" );
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document.write( "(n/2)(n - 3) = 65\r<BR>\n" );
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document.write( "I then set up another equation to look like this:\r<BR>\n" );
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document.write( "(n/2)(n - 3) = 80\r<BR>\n" );
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document.write( "I now need to solve each equation for n. \r<BR>\n" );
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document.write( "Yes?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845380 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=845380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You have the correct equation for each part.\r<BR>\n" );
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document.write( "(n/2)(n - 3) = 65 solves to n = -10 and n = 13<BR>\n" );
document.write( "Ignore the negative answer. A negative number of sides doesn't make sense.<BR>\n" );
document.write( "n = 13 is the only solution<BR>\n" );
document.write( "Therefore a 13 sided polygon has 65 diagonals.\r<BR>\n" );
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document.write( "(n/2)(n - 3) = 80 produces two non-integer solutions (roughly n = -11.2377 and n = 14.2377)<BR>\n" );
document.write( "This will mean there aren't any polygons that have 80 diagonals.\r<BR>\n" );
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document.write( "Refer to the link below to see what the step-by-step process looks like.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Polygons/Polygons.faq.question.1199136.html\">https://www.algebra.com/algebra/homework/Polygons/Polygons.faq.question.1199136.html</a>\r<BR>\n" );
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document.write( "If you have questions about any of the steps I mentioned, then please let me know.<BR>\n" );
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