document.write( "Question 1189025: ΔABC is an isosceles right triangle with AC=4√3. F is the mid-point of hypotenuse AC, and ΔDEF is equilateral. Find the perimeter of ΔDEF.
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Algebra.Com's Answer #820250 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll pirate Greenestamps picture\r\n" );
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\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "By the law of sines,\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2Fsin%28C%29\"\"%22%22=%22%22\"\"FC%2Fsin%28%22%3CFEC%22%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2Fsin%2845%5Eo%29\"\"%22%22=%22%22\"\"2sqrt%283%29%2Fsin%2875%5Eo%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2Asin%2875%5Eo%29\"\"%22%22=%22%22\"\"2sqrt%283%29sin%2845%5Eo%29\"\r\n" ); document.write( "\r\n" ); document.write( "We know sin(45o), we must find sin(75o).\r\n" ); document.write( "\r\n" ); document.write( "\"sin%2875%5Eo%29\"\"%22%22=%22%22\"\"sin%2845%5Eo%2B30%5Eo%29\"\"%22%22=%22%22\"\"sin%2845%5Eo%29cos%2830%5Eo%29%2Bcos%2845%5Eo%29sin%2830%5Eo%29\"\"%22%22=%22%22\"\r\n" ); document.write( "\"%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29%2B%28sqrt%282%29%2F2%29%281%2F2%29\"\"%22%22=%22%22\"\"sqrt%286%29%2F4%2Bsqrt%282%29%2F4\"\"%22%22=%22%22\"\"%28sqrt%286%29%2Bsqrt%282%29%29%2F4\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2A%28%28sqrt%286%29%2Bsqrt%282%29%29%2F4%29%29\"\"%22%22=%22%22\"\"2sqrt%283%29%2A%28sqrt%282%29%2F2%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2A%28sqrt%286%29%2Bsqrt%282%29%29%2F4%29%29\"\"%22%22=%22%22\"\"2sqrt%283%29%28sqrt%282%29%2F2%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2A%28%28sqrt%286%29%2Bsqrt%282%29%29%2F4%29%29\"\"%22%22=%22%22\"\"sqrt%286%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF%2A%28%28sqrt%286%29%2Bsqrt%282%29%29%29%29\"\"%22%22=%22%22\"\"4%2Asqrt%286%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"4sqrt%286%29%2F%28%28sqrt%286%29%2Bsqrt%282%29%29%29%29\"\r\n" ); document.write( "\r\n" ); document.write( "Rationalize the denominator:\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"%284sqrt%286%29%29%2F%28+%28sqrt%286%29%2Bsqrt%282%29+%29%29\"\"%22%22%2A%22%22\"\"%28sqrt%286%29-sqrt%282%29%29%2F%28sqrt%286%29-sqrt%282%29%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"%28++4sqrt%286%29%28sqrt%286%29-sqrt%282%29%29%29%2F%286-2%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"%284sqrt%286%29%28sqrt%286%29-sqrt%282%29%29%29%2F%284%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"sqrt%286%29%28sqrt%286%29-sqrt%282%29%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"6-sqrt%2812%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"6-sqrt%284%2A3%29\"\r\n" ); document.write( "\r\n" ); document.write( "\"EF\"\"%22%22=%22%22\"\"6-2sqrt%283%29\"\"%22%22=%22%22\"\"2%283-sqrt%283%29%29\"\r\n" ); document.write( "\r\n" ); document.write( "Since ΔDEF is equilateral, its perimeter is 3 times its side EF.\r\n" ); document.write( "\r\n" ); document.write( "Perimeter of ΔDEF = \"6%283-sqrt%283%29%29\", choice A)\r\n" ); document.write( "\r\n" ); document.write( "Edwin

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