document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009832>Question 1009832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of sides of each of the two polygons if the total number of sides of the polygons is 13, and the sum of the number of diagonals is 25. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625436 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=625436\">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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sides of one of the two polygons<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sides of the other polygons<BR>\n" );
document.write( "Since it does not matter which is the one and which is the other, we will find two solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the same two solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13 ALIGN=MIDDLE  ALT=\"x%2By=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > , because \"the total number of sides of the polygons is 13\".<BR>\n" );
document.write( "The number of diagonals of 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 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-3%29%2An%2F2 ALIGN=MIDDLE  ALT=\"%28n-3%29%2An%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so \"the sum of the number of diagonals is 25\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2Ax%2F2%2B%28y-3%29%2Ay%2F2=25 ALIGN=MIDDLE  ALT=\"%28x-3%29%2Ax%2F2%2B%28y-3%29%2Ay%2F2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2Ax%2B%28y-3%29%2Ay=50 ALIGN=MIDDLE  ALT=\"%28x-3%29%2Ax%2B%28y-3%29%2Ay=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=13%2C%28x-3%29%2Ax%2B%28y-3%29%2Ay=50%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=13%2C%28x-3%29%2Ax%2B%28y-3%29%2Ay=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13 ALIGN=MIDDLE  ALT=\"x%2By=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13-x ALIGN=MIDDLE  ALT=\"y=13-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2Ax%2B%28y-3%29%2Ay=50 ALIGN=MIDDLE  ALT=\"%28x-3%29%2Ax%2B%28y-3%29%2Ay=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2Ax%2B%2813-x-3%29%2813-x%29=50 ALIGN=MIDDLE  ALT=\"%28x-3%29%2Ax%2B%2813-x-3%29%2813-x%29=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B%2810-x%29%2813-x%29=50 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B%2810-x%29%2813-x%29=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B130-10x-13x%2Bx%5E2=50 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B130-10x-13x%2Bx%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-26x%2B130=50 ALIGN=MIDDLE  ALT=\"2x%5E2-26x%2B130=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-26x%2B80=0 ALIGN=MIDDLE  ALT=\"2x%5E2-26x%2B80=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-13x%2B40=0 ALIGN=MIDDLE  ALT=\"x%5E2-13x%2B40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x-8%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=8%2C%22or%22%2Cx=5%29 ALIGN=MIDDLE  ALT=\"system%28x=8%2C%22or%22%2Cx=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those are the two solutions.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13-x=8 ALIGN=MIDDLE  ALT=\"y=13-x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13-8=5 ALIGN=MIDDLE  ALT=\"y=13-8=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "One polygon has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%285%29 ALIGN=MIDDLE  ALT=\"highlight%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides, and the other one has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );