document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483998>Question 483998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a regular pentagon, lines are drawn so that every possible pair of vertices are connected. How many triangles are in the resulting figure?\r<BR>\n" );
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document.write( "choose the answer and explain the reason to choose your response<BR>\n" );
document.write( "35<BR>\n" );
document.write( "30<BR>\n" );
document.write( "20<BR>\n" );
document.write( "25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331314 by </B><A HREF=/tutors/aboutme.mpl?userid=chessace><B>chessace(471)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chessace><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=chessace><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The major problem with this is to avoid counting a triangle twice.<BR>\n" );
document.write( "Each edge has a small triangle with no cross lines: 5<BR>\n" );
document.write( "Each vertex has a small triange with no cross lines: 5<BR>\n" );
document.write( "Each edge has 2 triangles with 1 cross line (its small triagle merged with one of the small triagles of its 2 vertices): 10<BR>\n" );
document.write( "Each vertex (using its 2 original edges) has a triangle with 2 cross lines: 5<BR>\n" );
document.write( "Each original edge to the opposite vertex has a triangle with 5 little cross lines: 5<BR>\n" );
document.write( "Total = 30.<BR>\n" );
document.write( "The previously posted solution counted the small triangle by an edge twice, hence over by 5.<BR>\n" );
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