document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158597>Question 1158597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections. (a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle?<BR>\n" );
document.write( "(b) If the sections are 1 ft and 5 ft long, will the sticks form a triangle?<BR>\n" );
document.write( "(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781542 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "One stick is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3ft ALIGN=MIDDLE  ALT=\"3ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > long and another is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6ft ALIGN=MIDDLE  ALT=\"6ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > long. You break the longer stick into sections.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " (a) If the sections are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ft ALIGN=MIDDLE  ALT=\"2ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4ft ALIGN=MIDDLE  ALT=\"4ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > long, will the sticks form a triangle?\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2+ ALIGN=MIDDLE  ALT=\"a=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3+ ALIGN=MIDDLE  ALT=\"b=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "recall: The Triangle Inequality Theorem states that the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum ALIGN=MIDDLE  ALT=\"sum\"   DISABLED_style= \"max-width:90%; height:auto;\" > of any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides of a triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=must ALIGN=MIDDLE  ALT=\"must\"   DISABLED_style= \"max-width:90%; height:auto;\" > be greater than the measure of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=third+ ALIGN=MIDDLE  ALT=\"third+\"   DISABLED_style= \"max-width:90%; height:auto;\" >side.\r<BR>\n" );
document.write( "\n" );
document.write( "so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%3Ec ALIGN=MIDDLE  ALT=\"a%2Bb%3Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B3%3E4 ALIGN=MIDDLE  ALT=\"2%2B3%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3E4 ALIGN=MIDDLE  ALT=\"5%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->true<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc%3Eb ALIGN=MIDDLE  ALT=\"a%2Bc%3Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B4%3E3 ALIGN=MIDDLE  ALT=\"2%2B4%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%3E3 ALIGN=MIDDLE  ALT=\"6%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc%3Ea ALIGN=MIDDLE  ALT=\"b%2Bc%3Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B4%3E2 ALIGN=MIDDLE  ALT=\"3%2B4%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%3E2 ALIGN=MIDDLE  ALT=\"7%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->true\r<BR>\n" );
document.write( "\n" );
document.write( "=> the sticks <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=will ALIGN=MIDDLE  ALT=\"will\"   DISABLED_style= \"max-width:90%; height:auto;\" > form a triangle\r<BR>\n" );
document.write( "\n" );
document.write( "(b) If the sections are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1ft ALIGN=MIDDLE  ALT=\"1ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5ft ALIGN=MIDDLE  ALT=\"5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > long, will the sticks form a triangle?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1+ ALIGN=MIDDLE  ALT=\"a=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5+ ALIGN=MIDDLE  ALT=\"b=5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%3Ec ALIGN=MIDDLE  ALT=\"a%2Bb%3Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B5%3E4 ALIGN=MIDDLE  ALT=\"1%2B5%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%3E4 ALIGN=MIDDLE  ALT=\"6%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> false<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc%3Eb ALIGN=MIDDLE  ALT=\"a%2Bc%3Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4%3E5 ALIGN=MIDDLE  ALT=\"1%2B4%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3E5 ALIGN=MIDDLE  ALT=\"5%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->false<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc%3Ea ALIGN=MIDDLE  ALT=\"b%2Bc%3Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B4%3E1 ALIGN=MIDDLE  ALT=\"5%2B4%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%3E1 ALIGN=MIDDLE  ALT=\"9%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true\r<BR>\n" );
document.write( "\n" );
document.write( "since two false => the sticks will <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > form a triangle\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?\r<BR>\n" );
document.write( "\n" );
document.write( " the probability that they form a triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or r approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.67 ALIGN=MIDDLE  ALT=\"16.67\"   DISABLED_style= \"max-width:90%; height:auto;\" >%\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );