document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328662>Question 328662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What polygon has 3 times as many diagonals as sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235559 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of diagonals in a polygon is given by the equation:\r<BR>\n" );
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document.write( "d = s * (s-3) / 2\r<BR>\n" );
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document.write( "d is the number of diagonals.<BR>\n" );
document.write( "s is the number of sides.\r<BR>\n" );
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document.write( "A triangle has 3 * 0 / 2 diagonals = 0<BR>\n" );
document.write( "A rectangle has 4 * 1 / 2 = 3<BR>\n" );
document.write( "A pentagon has 5 * 2 / 2 = 5<BR>\n" );
document.write( "A hexagon has 6 * 3 / 2 = 9\r<BR>\n" );
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document.write( "The question is what polygon had 3 times as many diagonals as sides.\r<BR>\n" );
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document.write( "The formula would be d = 3 * s\r<BR>\n" );
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document.write( "Since d = s * (s-3) / 2, then this formula becomes:\r<BR>\n" );
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document.write( "s * (s-3)/2 = 3 * s\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "s * (s-3) = 6 * s\r<BR>\n" );
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document.write( "Divide both sides of this equation by s to get:\r<BR>\n" );
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document.write( "s-3 = 6\r<BR>\n" );
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document.write( "Add 3 to both sides of this equation to get:\r<BR>\n" );
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document.write( "s = 9\r<BR>\n" );
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document.write( "This suggests that a polygon with 9 sides will have 3 times the number of diagonals as sides.\r<BR>\n" );
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document.write( "The formula for the number of diagonals is:\r<BR>\n" );
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document.write( "d = s * (s-3) / 2\r<BR>\n" );
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document.write( "Let s = 9 and this formula becomes:\r<BR>\n" );
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document.write( "d = 9 * 6 / 2 which becomes d = 54 / 2 which becomes d = 27\r<BR>\n" );
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document.write( "since 27 = 3 * 9, then this is your answer.\r<BR>\n" );
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document.write( "The polygon with 9 sides will have 3 times the number of diagonals as sides.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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