document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=429889>Question 429889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the side length of a equilateral triangle with an area of 12 radical 3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298603 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=298603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One of the other tutors mis-applied Heron's formula. Instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%28%28p-a%29%28p-b%29%28p-c%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%28%28p-a%29%28p-b%29%28p-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%28p%28p-a%29%28p-b%29%28p-c%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%28p%28p-a%29%28p-b%29%28p-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Heron's formula works, but it is somewhat tedious. Also, we could use the standard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+bh%2F2 ALIGN=MIDDLE  ALT=\"A+=+bh%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > but that is boring, and there are faster solutions.\r<BR>\n" );
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document.write( "We can let the side length of the triangle be x. We can write the area in terms of two of the side lengths and the angle in between, i.e.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Asin%2860%29%2F2+=+12sqrt%283%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Asin%2860%29%2F2+=+12sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Asin%2860%29+=+24sqrt%283%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Asin%2860%29+=+24sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2860%29+=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%2860%29+=+sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Asqrt%283%29%2F2+=+24sqrt%283%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Asqrt%283%29%2F2+=+24sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+48 ALIGN=MIDDLE  ALT=\"x%5E2+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2848%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, approximately 6.928. </SPAN>\n" );
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