document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105588>Question 1105588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27&#8730;3 cm2. What is the side lenght AB, in cm?<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 #720489 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C275%2C-0.6%2C0.6%2C-0.1%2C1%2C%0D%0Atriangle%28-0.5%2C0%2C0.5%2C0%2C0%2C0.866%29%2C%0D%0Atriangle%280%2C0%2C0.25%2C0%2C0%2C0.866%29%2C%0D%0Arectangle%280%2C0%2C-0.05%2C0.05%29%2C%0D%0Alocate%280.5%2C0%2CB%29%2Clocate%28-0.53%2C0%2CC%29%2C%0D%0Alocate%280.24%2C0%2CE%29%2Clocate%28-0.01%2C0%2CD%29%2Clocate%28-0.01%2C0.92%2CA%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "An equilateral triangle with side length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29x ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ",<BR>\n" );
document.write( "and an area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F4%29x%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F4%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the length of side AB in cm, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F4%29x%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F4%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the area of ABC in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The altitude of an equilateral triangle is also a median,<BR>\n" );
document.write( "so it splits the triangle into two triangles with the same area.<BR>\n" );
document.write( "Those triangles are ABD and ACD, each with an area equal to {1/2}}} of the area of ABC.<BR>\n" );
document.write( "Triangle ABD is similarly split into triangles ABE and AED,<BR>\n" );
document.write( "each with area equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >of the area of ABD,<BR>\n" );
document.write( "meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of ABC.<BR>\n" );
document.write( "Triangle ARC is the union of triangles ABD and AED,<BR>\n" );
document.write( "so its area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B1%2F4=3%2F4 ALIGN=MIDDLE  ALT=\"1%2F2%2B1%2F4=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of ABC.<BR>\n" );
document.write( "That is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%28sqrt%283%29%2F4%29x%5E2=%283sqrt%283%29%2F16%29x%5E2 ALIGN=MIDDLE  ALT=\"%283%2F4%29%28sqrt%283%29%2F4%29x%5E2=%283sqrt%283%29%2F16%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283sqrt%283%29%2F16%29x%5E2=27sqrt%283%29 ALIGN=MIDDLE  ALT=\"%283sqrt%283%29%2F16%29x%5E2=27sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F16%29x%5E2=27 ALIGN=MIDDLE  ALT=\"%283%2F16%29x%5E2=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=27%2A16%2F3 ALIGN=MIDDLE  ALT=\"x%5E2=27%2A16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=9%2A16 ALIGN=MIDDLE  ALT=\"x%5E2=9%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%289%2A16%29=sqrt%289%29sqrt%2816%29r3%2A4=highlight%2812%29 ALIGN=MIDDLE  ALT=\"x=sqrt%289%2A16%29=sqrt%289%29sqrt%2816%29r3%2A4=highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The length of side AB is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812cm%29 ALIGN=MIDDLE  ALT=\"highlight%2812cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );