document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247152>Question 247152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of a triangle that has sides of length 5, 6, and 7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180359 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=180359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> area of a triangle equals 1/2 * b * h\r<BR>\n" );
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document.write( "from your triangle, I don't think we can find the base very easily.\r<BR>\n" );
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document.write( "fortunately there is a formula that allows you to find the area of a triangle when you only know the sides.\r<BR>\n" );
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document.write( "It's called Heron's formula.\r<BR>\n" );
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document.write( "that formula is:\r<BR>\n" );
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document.write( "Area of a Triangle = sqrt((s*(s-a)*(s-b)*(s-c)),\r<BR>\n" );
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document.write( "where s=(a+b+c)/2 which is the same as p/2 where p equals the perimeter of the triangle.\r<BR>\n" );
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document.write( "assuming that c is the base of the triangle, Heron's formula allows us to find the height of the triangle as well.\r<BR>\n" );
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document.write( "That formula would be:\r<BR>\n" );
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document.write( "h = (2 * (SQRT(s(s-a)(s-b)(s-c))) / 2\r<BR>\n" );
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document.write( "I believe this comes from the fact that A = 1/2 * b * h, so if we solve for h, we get h = 2*A/b\r<BR>\n" );
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document.write( "In your triangle:\r<BR>\n" );
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document.write( "s = (5+6+7)/2 = 18/2 = 9\r<BR>\n" );
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document.write( "In your triangle:\r<BR>\n" );
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document.write( "A = sqrt(9 * (9-5) * (9-6) * (9-7)) which equals:\r<BR>\n" );
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document.write( "sqrt (9 * 4 * 3 * 2) which equals:\r<BR>\n" );
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document.write( "sqrt (216) which equals:\r<BR>\n" );
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document.write( "14.69693846\r<BR>\n" );
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document.write( "Since A = 14.69693846, then h = 2/c * 14.69693846 = 2/7 * 14.69693846 = 4.199125273\r<BR>\n" );
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document.write( "If A = 1/2 * b * h, then A = 1/2 * 7 * 4.199125273 = 14.69693846 which is back where we started from.\r<BR>\n" );
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document.write( "You can check Heron's formula for yourself by selecting the following link.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://mste.illinois.edu/dildine/heron/triarea.html\" target = \"_blank\">http://mste.illinois.edu/dildine/heron/triarea.html</a>\r<BR>\n" );
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