document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737271>Question 737271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear : The tutor<BR>\n" );
document.write( "I cant interpret this question ,kindly help me out<BR>\n" );
document.write( "How many different triangles can be made with a perimeter of 12matches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450299 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=450299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a triangle can be found using:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+a+%2B+b+%2B+c ALIGN=MIDDLE  ALT=\"P+=+a+%2B+b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the lengths of the sides of the triangle.\r<BR>\n" );
document.write( "\n" );
document.write( "You also have the rules:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%3E+c ALIGN=MIDDLE  ALT=\"a+%2B+b+%3E+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+c+%3E+b ALIGN=MIDDLE  ALT=\"a+%2B+c+%3E+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+c+%3E+a ALIGN=MIDDLE  ALT=\"b+%2B+c+%3E+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "These are true for all triangles.<BR>\n" );
document.write( "The most important thing to be kept in mind is the triangle inequality theorem that says that the sum of any two sides is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=greater ALIGN=MIDDLE  ALT=\"greater\"   DISABLED_style= \"max-width:90%; height:auto;\" > than the third side \r<BR>\n" );
document.write( "\n" );
document.write( "If the sides do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfy+ ALIGN=MIDDLE  ALT=\"satisfy+\"   DISABLED_style= \"max-width:90%; height:auto;\" >this theorem, then the triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=possible ALIGN=MIDDLE  ALT=\"possible\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "this is also good to remember:<BR>\n" );
document.write( "first triangle among many triangles with perimeter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the most famous is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-4-5 ALIGN=MIDDLE  ALT=\"3-4-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangle, the triangle with sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or a similar one.) Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+%2B+4%5E2+=+5%5E2 ALIGN=MIDDLE  ALT=\"3%5E2+%2B+4%5E2+=+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we are assured by the converse of the Pythagorean theorem that the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-4-5 ALIGN=MIDDLE  ALT=\"3-4-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangle is right.\r<BR>\n" );
document.write( "\n" );
document.write( "so, first solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+3+%2B+5+=+12 ALIGN=MIDDLE  ALT=\"4+%2B+3+%2B+5+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Keeping this in mind we get the following combinations:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+2+%2B+5+=+12 ALIGN=MIDDLE  ALT=\"5+%2B+2+%2B+5+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B2%3E5 ALIGN=MIDDLE  ALT=\"5%2B2%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfies+ ALIGN=MIDDLE  ALT=\"satisfies+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  theorem,  the triangle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=possible ALIGN=MIDDLE  ALT=\"possible\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+4+%2B+4+=+12 ALIGN=MIDDLE  ALT=\"4+%2B+4+%2B+4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B4%3E4 ALIGN=MIDDLE  ALT=\"4%2B4%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfies+ ALIGN=MIDDLE  ALT=\"satisfies+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  theorem,  the triangle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=possible ALIGN=MIDDLE  ALT=\"possible\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+12 ALIGN=MIDDLE  ALT=\"P+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the possible triangles, written <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B+b%2Bc ALIGN=MIDDLE  ALT=\"a%2B+b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+3+%2B+5+=+12 ALIGN=MIDDLE  ALT=\"4+%2B+3+%2B+5+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+2+%2B+5+=+12 ALIGN=MIDDLE  ALT=\"5+%2B+2+%2B+5+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+4+%2B+4+=+12 ALIGN=MIDDLE  ALT=\"4+%2B+4+%2B+4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );