document.write( "Question 251486: In a triangle, the lengths of three medians are 4, 5 and 6, find the area of the triangle. \n" ); document.write( "
Algebra.Com's Answer #183155 by Theo(13342)\"\" \"About 
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area of a triangle in terms of the median is expressed as follows:\r
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\n" ); document.write( "\n" ); document.write( "The area of a triangle can be expressed in terms of the medians by:\r
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\n" ); document.write( "\n" ); document.write( "\"A+=+%284%2F3%29+%2A+sqrt%28sm%28sm-m1%29%28sm-m2%29%28sm-m3%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "where:\r
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\n" ); document.write( "\n" ); document.write( "\"sm+=+%281%2F2%29+%2A+%28m1%2Bm2%2Bm3%29\". \r
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\n" ); document.write( "\n" ); document.write( "see http://mathworld.wolfram.com/TriangleMedian.html for details.\r
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\n" ); document.write( "\n" ); document.write( "in terms of your problem:\r
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\n" ); document.write( "\n" ); document.write( "m1 = 4
\n" ); document.write( "m2 = 5
\n" ); document.write( "m3 = 6
\n" ); document.write( "\"sm+=+%281%2F2%29%2A%284%2B5%2B6%29+=+%281%2F2%29+%2A+%2815%29+=+7.5\"\r
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\n" ); document.write( "\n" ); document.write( "area of the triangle is therefore:\r
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\n" ); document.write( "\n" ); document.write( "\"A=%284%2F3%29+%2A+sqrt%28%28sm%29+%2A+%28sm-m1%29+%2A+%28sm-m2%29+%2A+%28sm-m3%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "this becomes:\r
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\n" ); document.write( "\n" ); document.write( "\"A=%284%2F3%29+%2A+sqrt%28%287.5%29+%2A+%287.5-4%29+%2A+%287.5-5%29+%2A+%287.5-6%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "which becomes:\r
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\n" ); document.write( "\n" ); document.write( "\"A=%284%2F3%29+%2A+sqrt%28%287.5%29+%2A+%283.5%29+%2A+%282.5%29+%2A+%281.5%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "which becomes:\r
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\n" ); document.write( "\n" ); document.write( "\"A=%284%2F3%29+%2A+sqrt%2898.4375%29\"\r
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\n" ); document.write( "\n" ); document.write( "which becomes\r
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\n" ); document.write( "\n" ); document.write( "A = 13.22875656\r
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\n" ); document.write( "\n" ); document.write( "here's another reference:\r
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\n" ); document.write( "\n" ); document.write( "http://www.math10.com/en/geometry/median.html\r
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\n" ); document.write( "\n" ); document.write( "here's yet another.\r
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\n" ); document.write( "\n" ); document.write( "http://pballew.net/medians.htm\r
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