document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003640>Question 1003640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> polygon k has 36 more diagonals and 3 more sides than polygon L. How many sides do each of these polygons have </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620305 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sides of the polygon K.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B3 ALIGN=MIDDLE  ALT=\"k%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sides of polygon L.\r<BR>\n" );
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document.write( "A polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertices.<BR>\n" );
document.write( "Each vertex can be connected to each of the other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1 ALIGN=MIDDLE  ALT=\"n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertices by a segment.<BR>\n" );
document.write( "Two of those segments will be sides, connecting adjacent vertices.<BR>\n" );
document.write( "The other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1-2=n-3 ALIGN=MIDDLE  ALT=\"n-1-2=n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > segments will be diagonals.<BR>\n" );
document.write( "Each of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertices is involved in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3 ALIGN=MIDDLE  ALT=\"n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > diagonals,<BR>\n" );
document.write( "but since each diagonal involves <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertices,<BR>\n" );
document.write( "the total number of diagonals for polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-3%29%2F2 ALIGN=MIDDLE  ALT=\"n%28n-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "The total number of diagonals for polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28k-3%29%2F2 ALIGN=MIDDLE  ALT=\"k%28k-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The total number of diagonals for polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B3 ALIGN=MIDDLE  ALT=\"k%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B3%29k%2F2 ALIGN=MIDDLE  ALT=\"%28k%2B3%29k%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The problem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B3%29k%2F2=36%2Bk%28k-3%29%2F2 ALIGN=MIDDLE  ALT=\"%28k%2B3%29k%2F2=36%2Bk%28k-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B3%29k%2F2=36%2Bk%28k-3%29%2F2 ALIGN=MIDDLE  ALT=\"%28k%2B3%29k%2F2=36%2Bk%28k-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B3%29k=72%2Bk%28k-3%29 ALIGN=MIDDLE  ALT=\"%28k%2B3%29k=72%2Bk%28k-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%2B3k=72%2Bk%5E2-3k%29 ALIGN=MIDDLE  ALT=\"k%5E2%2B3k=72%2Bk%5E2-3k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3k=72-3k%29 ALIGN=MIDDLE  ALT=\"3k=72-3k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6k=72%29 ALIGN=MIDDLE  ALT=\"6k=72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=72%2F6%29 ALIGN=MIDDLE  ALT=\"k=72%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=12%29 ALIGN=MIDDLE  ALT=\"k=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B3=15 ALIGN=MIDDLE  ALT=\"k%2B3=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Polygon K has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%29 ALIGN=MIDDLE  ALT=\"highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides, and polygon L has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815%29 ALIGN=MIDDLE  ALT=\"highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides. </SPAN>\n" );
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