document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541701>Question 541701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of 2 sides of a triangle are 4 and 9. What is the range of possible lengths for the 3rd side?\r<BR>\n" );
document.write( "\n" );
document.write( "How do you set up these problems, and how do you solve them? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354250 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">This kind of triangle problem is fairly simple.<br><BR>\n" );
document.write( "There is a rule for triangle side lengths.<br><BR>\n" );
document.write( "Each leg must be between the difference and sum of the other two legs (non-inclusively).<br><BR>\n" );
document.write( "So, since your two legs are 4 and 9, we have: <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-4%3Cs%3C9%2B4 ALIGN=MIDDLE  ALT=\"9-4%3Cs%3C9%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3Cs%3C13 ALIGN=MIDDLE  ALT=\"5%3Cs%3C13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Therefore the possible length of the third side of your triangle would be:<br><BR>\n" );
document.write( "any real number between 5 and 13 (not including 5 and 13 of course).  Or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3Cs%3C13 ALIGN=MIDDLE  ALT=\"5%3Cs%3C13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If the 3rd side of your triangle was 5 or 13, it would be a degenerate triangle which appeared to be a straight line.<br><BR>\n" );
document.write( "I hope this helps!<br><br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );