document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21445>Question 21445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At point P inside an equilateral triangle are connected to the vertices are 4, 5 and 6 respectively. Find the length of one side. all sides are equal sine it is equilateral. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10339 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I AM GIVING THE SOLUTION HERE ,BUT WOULD LIKE TO KNOW YOUR PRESENT COURSE OF STUDY AND YOUR PRESENT AWARENESS OF THE SUBJECT TO GIVE YOU A BETTER SOLUTION IF POSSIBLE<BR>\n" );
document.write( "LET ABC BE THE EQUILATERAL TRIANGLE WITH SIDE=2A...LET P BE A POINT INSIDE THE TRIANGLE.JOIN PA,PB,PC.SINCE P IS INSIDE THE TRIANGLE WE CAN WRITE THAT<BR>\n" );
document.write( "AREA.ABC =AREA.PBC+AREA.PCA+AREA.PAB <BR>\n" );
document.write( "SINCE ABC IS EQUILATERAL TRIANGLE ITS AREA IS GIVEN BY SIDE*SIDE*SQ.RT3/4<BR>\n" );
document.write( "=2A*2A*SQRT3/4=A*A*SQ.RT3<BR>\n" );
document.write( "AREA OF A TRIANGLE IS GIVEN BY SQRT.OF{S(S-A)(S-B)(S-C)}WHERE S IS SEMIPERIMETER OF TRIANGLE{(A+B+C)/2},WITH A,B,C,AS ITS SIDES .<BR>\n" );
document.write( "PBC HAS SIDES OF 2A,4,5<BR>\n" );
document.write( "PCA HAS SIDES OF 2A,5,6<BR>\n" );
document.write( "PAB HAS SIDES OF 2A,6,4<BR>\n" );
document.write( "SO WITH THE ABOVE FORMULA WE GET \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2ASQRT%283%29 ALIGN=MIDDLE  ALT=\"A%5E2%2ASQRT%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%284.5%2BA%29%2A%284.5-A%29%2A%28A%2B0.5%29%2A%28A-0.5%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%284.5%2BA%29%2A%284.5-A%29%2A%28A%2B0.5%29%2A%28A-0.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%285.5%2BA%29%2A%285.5-A%29%2A%28A%2B0.5%29%2A%28A-0.5%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%285.5%2BA%29%2A%285.5-A%29%2A%28A%2B0.5%29%2A%28A-0.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%285%2BA%29%2A%285-A%29%2A%28A%2B1%29%2A%28A-1%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%285%2BA%29%2A%285-A%29%2A%28A%2B1%29%2A%28A-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2ASQRT%283%29 ALIGN=MIDDLE  ALT=\"A%5E2%2ASQRT%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%2820.25-A%5E2%29%2A%28A%5E2-0.25%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%2820.25-A%5E2%29%2A%28A%5E2-0.25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%2830.25-A%5E2%29%2A%28A%5E2-0.25%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%2830.25-A%5E2%29%2A%28A%5E2-0.25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SQRT%28%2825-A%5E2%29%2A%28A%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"SQRT%28%2825-A%5E2%29%2A%28A%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "FROM  THIS WE CAN SOLVE FOR A AND HENCE FIND THE SIDE OF THE TRIANGLE ...OFCOURSE IT IS A COMPLEX PROCESS..AND FOR YOU THE EASIEST WAY WOULD BE TO GO BY A GOAL SEEK TOOL USING XL IF YOU ARE FAMILIAR ..THE ANSWER IS THAT THE SIDE OF EQUILATERAL TRIANGLE =2A=8.5364\r<BR>\n" );
document.write( "\n" );
document.write( "YOU CAN CHECK BY SUBSTITUTION IN THE ABOVE FOR MULA </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );