document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969603>Question 969603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the area of an equilateral triangle is 108 square root of 3 feet squared what is the length of a side and the apothem in simplest radical form? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592431 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Side=12 sqrt (3) feet; ap=6 feet  ANSWER\r<BR>\n" );
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document.write( "A=1/2 * bh\r<BR>\n" );
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document.write( "108 sqrt (3) sq ft=(1/2) bh\r<BR>\n" );
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document.write( "Equilateral triangles with side s  have an altitude of (s/2) sqrt (3).  The altitude splits the base into 2, so the triangle formed with the altitude is a 30-60-90 triangle with the hypotenuse s, the altitude is (s/2)sqrt(3).\r<BR>\n" );
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document.write( "Area is (1/2) *s *(s/2)*sqrt(3)=[(s^2)/4]sqrt (3)=108 sqrt (3)\r<BR>\n" );
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document.write( "The sqrt(3) on both sides divide out, \r<BR>\n" );
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document.write( "108=(s^2/4)<BR>\n" );
document.write( "Multiply by 4<BR>\n" );
document.write( "432= s^2<BR>\n" );
document.write( "s= sqrt (432)  In simple radical form would be sqrt (144*3)=12 sqrt(3) feet\r<BR>\n" );
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document.write( "The apothem is 1/3 the altitude.  or (1/3)*(s/2)sqrt(3)=(s/6)sqrt(3)\r<BR>\n" );
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document.write( "But s=12 sqrt (3)  so (s/6) sqrt (3)=12/6 (sqrt 3)^2=2*3 =6 feet\r<BR>\n" );
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document.write( "sqrt 3^2=3\r<BR>\n" );
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document.write( " </SPAN>\n" );
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