document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172767>Question 1172767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Equilateral triangle ABC has altitude AD of length 12 mm. Median AE of triangle ABD is drawn. What is the area of triangle AEC in mm²? </SPAN>\n" );
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document.write( "Triangles ABD and ACD are 30-60-90 right triangles, with long leg AD having length 12.  The side length of triangle ABC is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A%282%2Fsqrt%283%29%29+=+24%2Fsqrt%283%29+=+8%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"12%2A%282%2Fsqrt%283%29%29+=+24%2Fsqrt%283%29+=+8%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "AD is half that side length, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; ED is half again as much, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So the base of triangle AEC has length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Then the area is one-half base time height:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%286%2Asqrt%283%29%29%2812%29+=+36%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%286%2Asqrt%283%29%29%2812%29+=+36%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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