document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087861>Question 1087861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Point P is inside equilateral triangle ABC such that the altitudes from P to AB, BC, and CA have lengths 5, 6, and 7 respectively. What is the area of triangle ABC?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702135 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PA, PB, PC splits triangle ABC into three triangles<BR>\n" );
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document.write( "let s be the length of a side of equilateral triangle ABC<BR>\n" );
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document.write( "5s/2 + 6s/2 + 7s/2 = s^2 * square root(3) / 4 (area of equilateral triangle)<BR>\n" );
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document.write( "divide both sides of = by s<BR>\n" );
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document.write( "5/2 + 6/2 +7/2 = (s * square root(3)) / 4<BR>\n" );
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document.write( "multiply both sides of = by 4<BR>\n" );
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document.write( "10 + 12 + 14 = s * square root(3)<BR>\n" );
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document.write( "s = 36 / square root(3)<BR>\n" );
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document.write( "multiply the numerator and denominator by square root(3)<BR>\n" );
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document.write( "s = 36 * square root(3) / 3 = 12 * square root(3)<BR>\n" );
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document.write( "s^2 = (12 * square root(3))^2 = 144 * 3 = 432<BR>\n" );
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document.write( "area of ABC = (432 * square root(3) / 4)<BR>\n" );
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document.write( "area of ABC = 108 * square root(3)<BR>\n" );
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