document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461155>Question 461155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> GIVEN A TRIANGLE ABC WHERE THE VALUE OF BC^2 =370 UNITS AC^2 =74 AND AB^2=116 CALCULATE THE AREA OF A TRIANGLE /<BR>\n" );
document.write( " HINT; 370=9^2+17^2,74 = 5^2+7^2 AND 116 =4^2+10^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316310 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=316310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please refrain from caps lock...it gives the impression you are shouting your question.\r<BR>\n" );
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document.write( "We could attempt to find one of the angles using the law of cosines, then find the area using two sides and the in-between angle. However, this gets ugly, plus there is a way to take advantage of the \"hint.\"\r<BR>\n" );
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document.write( "We can plot the triangle on a Cartesian plane instead, such that it satisfies the requirements:\r<BR>\n" );
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document.write( "We see that, from the Pythagorean theorem, AC^2 = 7^2 + 5^2, etc.\r<BR>\n" );
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document.write( "To find the area of ABC, create a rectangle with sides parallel to the axes and with diagonal BC:\r<BR>\n" );
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document.write( "Next, we just subtract off areas from the big triangle. The area (denote by [ABC]) of triangle ABC is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE [ABC] = [CXBY] - [CXB] - [BAY] - [AYC]\">\r<BR>\n" );
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document.write( "The coordinates are all lattice points, so the areas are easy to evaluate.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE [ABC] = 153 - \frac{153}{2} - 34 - \frac{63}{2} = 11\"> (square units)\r<BR>\n" );
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