document.write( "Question 1150481: the sides of a triangle measure 21m, 27m, and 36m. a circle is drawn such its center lies on the 21m side and tangent to the remaining sides. find the radius of the circle. \n" ); document.write( "
Algebra.Com's Answer #771849 by ikleyn(52814)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "            This problem is to be solved in two steps.\r
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document.write( "Find the area of the triangle using the Heron's formula.\r\n" );
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document.write( "The perimeter is  P = 21+27+36 = 84 meters;  semi-perimeter is \"84%2F2\" = 42 meters.\r\n" );
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document.write( "According to the Heron's formula, the area of the triangle is\r\n" );
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document.write( "    \"sqrt%2842%2A%2842-21%29%2A%2842-27%29%2A%2842-36%29%29\" = \"sqrt%2842%2A21%2A15%2A6%29\" = \"21%2Asqrt%28180%29\" = \"21%2A2%2A3%2Asqrt%285%29\" = \"126%2Asqrt%285%29\"  square meters.\r\n" );
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document.write( "In the given triangle, connect the center of the semi-circle with the opposite vertex.\r\n" );
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document.write( "This segment will divide the given triangle in two smaller triangles.\r\n" );
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document.write( "For these smaller triangles, their bases are the sides of the length of 27 and 36 meters. The altitudes drawn to these bases \r\n" );
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document.write( "from the center of the semi-circle, are the radii of the semicircle.\r\n" );
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document.write( "So the area of the given triangle is equal to the sum of areas of the smaller triangles\r\n" );
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document.write( "    area = \"%281%2F2%29%2A27%2Ar\" + \"%281%2F2%29%2A36%2Ar\".\r\n" );
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document.write( "Thus you have this equation\r\n" );
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document.write( "    \"%281%2F2%29%2A27%2Ar\" + \"%281%2F2%29%2A36%2Ar\" = \"126%2Asqrt%285%29\".\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    27r + 36r = \"252%2Asqrt%285%29\",   63r = \"252%2Asqrt%285%29\",   r = \"%28252%2F63%29%2Asqrt%285%29\" = \"4%2Asqrt%285%29\" = 8.944 meters (approximately).\r\n" );
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document.write( "ANSWER.  The radius of the circle is  \"4%2Asqrt%285%29\" = 8.944 meters (approximately).\r\n" );
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