document.write( "Question 355204: A piece of wire (56 cm long) is cut into two pieces and each piece is bent into the shape of a square. If the sum of the areas of the two squares is 130 square cm, then how long was the shorter piece of the wire?\r
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Algebra.Com's Answer #253760 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We start with this piece of wire:\r\n" );
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document.write( "We cut it into two pieces of length x and 56-x \r\n" );
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document.write( "Then we bend the two pieces into squares, so that a side of each\r\n" );
document.write( "square is \"1%2F4\"th of the piece of wire, so we find the\r\n" );
document.write( "sides of the squares by dividing the length of the piece of wire\r\n" );
document.write( "by 4.\r\n" );
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document.write( "The area of the left square is \"%28x%2F4%29%5E2\" or \"x%5E2%2F4\" and the area of the right square is \"%28%2856-x%29%2F4%29%5E2\" or \"%2856-x%29%5E2%2F16\".\r\n" );
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document.write( "The sum of these two areas is 130 so we have the equation:\r\n" );
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document.write( "\"x%5E2%2F16%2B%2856-x%29%5E2%2F16+=+130\"\r\n" );
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document.write( "Multiplying through by 16\r\n" );
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document.write( "\"x%5E2%2B%2856-x%29%5E2+=+2080\"\r\n" );
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document.write( "\"x%5E2%2B%2856-x%29%2856-x%29=2080\"\r\n" );
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document.write( "\"x%5E2%2B3136-112x%2Bx%5E2=2080\"\r\n" );
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document.write( "\"2x%5E2-112x%2B1056=0\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"x%5E2-56x%2B528=0\"\r\n" );
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document.write( "That factors as \r\n" );
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document.write( "\"%28x-12%29%28x-44%29=0\"\r\n" );
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document.write( "So there are two solutions\r\n" );
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document.write( "x=12 and x=44\r\n" );
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document.write( "However they are really the same solution because\r\n" );
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document.write( "if we use x=12 for one piece the other piece is 56-12 or 44 and\r\n" );
document.write( "if we use x=44 for one piece the other piece is 56-44 or 12. So\r\n" );
document.write( "the second solution is just the case where the larger piece or\r\n" );
document.write( "wire were labeled x, and the smaller one 56-x.\r\n" );
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document.write( "So the shorter piece is 12 cm.\r\n" );
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document.write( "Incidentally the figures above are drawn to scale in accordance with\r\n" );
document.write( "this problem!\r\n" );
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document.write( "Edwin
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