document.write( "Question 847014: Gold Medal Problem
\n" ); document.write( "ABCD is a square. POints EFGH are teh midpoints of the sides. AB =1 inch. what is the area of the inside square region \n" ); document.write( "
Algebra.Com's Answer #510072 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Use the Pythagorean theorem on ΔDCG\r\n" );
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document.write( "DG² = DC² + CG²\r\n" );
document.write( "DG² = 1² + \"%281%2F2%29%5E2\"\r\n" );
document.write( "DG² = 1 + \"1%2F4\"\r\n" );
document.write( "DG² = \"5%2F4\"\r\n" );
document.write( "DG = \"sqrt%285%29%2F2\"\r\n" );
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document.write( "ΔDIH ∽ ΔDCG, therefore\r\n" );
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document.write( "\"ID%2F%28DH%29\"\"%22%22=%22%22\"\"DC%2FDG\"\r\n" );
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document.write( "ID×DG = DC×DH\r\n" );
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document.write( "ID\"%22%22%2Aexpr%28sqrt%285%29%2F2%29\"\"%22%22=%22%22\"\"1%2Aexpr%281%2F2%29\"\r\n" );
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document.write( "Multiply through by 2\r\n" );
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document.write( "ID\"sqrt%285%29\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "ID = \"1%2Fsqrt%285%29\" \r\n" );
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document.write( "Rationalize the denominator:\r\n" );
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document.write( "ID = \"1%2Fsqrt%285%29\"\"%22%22%2A%22%22\"\"sqrt%285%29%2Fsqrt%285%29\"\r\n" );
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document.write( "\"sqrt%285%29%2F5\" \r\n" );
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document.write( "ΔCJD ∽ ΔDCG, therefore,\r\n" );
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document.write( "\"JG%2F%28CG%29\"\"%22%22=%22%22\"\"CG%2FDG\"\r\n" );
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document.write( "JG×DG = CG×CG\r\n" );
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document.write( "JG\"%22%22%2Aexpr%28sqrt%285%29%2F2%29\"\"%22%22=%22%22\"\"expr%281%2F2%29%2Aexpr%281%2F2%29\"\r\n" );
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document.write( "JG\"%22%22%2Asqrt%285%29%2F2\"\"%22%22=%22%22\"\"expr%281%2F4%29\" \r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "2JG\"sqrt%285%29\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "JG = \"1%2F%282%2Asqrt%285%29%29\" = \"sqrt%285%29%2F10\"  (rationalizing)\r\n" );
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document.write( "DI + IJ + JG = DG\r\n" );
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document.write( "\"sqrt%285%29%2F5\" + IJ + \"sqrt%285%29%2F10\" = \"sqrt%285%29%2F2\"\r\n" );
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document.write( "Multiply through by 10\r\n" );
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document.write( "\"2%2Asqrt%285%29\" + 10·IJ + \"sqrt%285%29\" = \"5%2Asqrt%285%29\"\r\n" );
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document.write( "\"3%2Asqrt%285%29\" + 10·IJ = \"5%2Asqrt%285%29\"\r\n" );
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document.write( "                  10·IJ = \"2%2Asqrt%285%29\"\r\n" );
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document.write( "                     IJ = \"2%2Asqrt%285%29%2F10\"\r\n" );
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document.write( "                     IJ = \"sqrt%285%29%2F5\"\r\n" );
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document.write( "So the area of the inner square is IJ² = \"%28sqrt%285%29%2F5%29%5E2\" = \"5%2F25\" = \"1%2F5\" \r\n" );
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document.write( "Edwin
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