document.write( "Question 590102: How do you find the side lengths of a triangle when you have the perimeter OR the area, and the ratios of the sides. Example of a problem. Triangle ABC. AB has a scale of 2. BC has a scale of 4 and CA has a scale of 5. The area of the triangle is 450 cm2.\r
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Algebra.Com's Answer #375041 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
AB has a scale of 2. BC has a scale of 4 and CA has a scale of 5.
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document.write( "Let k be the constant that you have to multiply 2 by to get the length of AB,\r\n" );
document.write( "4 by to get the lebnth of BC, and 5 by to get the kength of CA \r\n" );
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document.write( "AB = 2k, BC = 4k, CA = 5k\r\n" );
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document.write( "Now we use Heron's formula for the area:\r\n" );
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document.write( "Area = \"sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29\"\r\n" );
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document.write( "a = AB = 2k, b = BC = 4k, c = CA = 5k\r\n" );
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document.write( "s = semiperimeter = \"%28a%2Bb%2Bc%29%2F2\" = \"%28AB%2BBC%2BCA%29%2F2\" = \"%282k%2B4k%2B5k%29%2F2\" = \"%2811k%29%2F2\"\r\n" );
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document.write( "s-a = \"%2811k%29%2F2\"-2k = \"%2811k%29%2F2\"-\"%284k%29%2F2\" =\"7k%2F2\"\r\n" );
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document.write( "s-b = \"%2811k%29%2F2\"-4k = \"%2811k%29%2F2\"-\"%288k%29%2F2\" =\"3k%2F2\"\r\n" );
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document.write( "s-c = \"%2811k%29%2F2\"-5k = \"%2811k%29%2F2\"-\"%2810k%29%2F2\" =\"k%2F2\"\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "Area = \"sqrt%28s%2A%28s-a%29%28s-b%29%28s-c%29%29\"\r\n" );
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document.write( "450 = \"sqrt%28expr%2811k%2F2%29%2Aexpr%287k%2F2%29%2Aexpr%283k%2F2%29%2Aexpr%28k%2F2%29%29\"\r\n" );
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document.write( "450 = \"sqrt%28231k%5E4%2F16%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "202500 = \"231k%5E4%2F16\"\r\n" );
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document.write( "Multiply both sides by 16\r\n" );
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document.write( "3240000 = 231k4\r\n" );
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document.write( "Divide both sides by 231\r\n" );
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document.write( "\"3240000%2F231\" = k4\r\n" );
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document.write( "Take fourth roots of both sides:\r\n" );
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document.write( "\"root%284%2C3240000%2F231%29\" = k\r\n" );
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document.write( "10.88261481 = k\r\n" );
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document.write( "AB = 2k = 2(10.88261481) = 21.76522962 \r\n" );
document.write( "BC = 4k = 4(10.88261481) = 43.53045924 \r\n" );
document.write( "CA = 5k = 5(10.88261481) = 54.41307405\r\n" );
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document.write( "[It's much easier if you are given the perimeter instead of the area]\r\n" );
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document.write( "Edwin
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