document.write( "Question 1099127: If the length of a rectangle is increased by 3times then the perimeter of a rectangle is 440meters and the area is 7200meter^2 .what is the real length of a rectangle
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Algebra.Com's Answer #713590 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let L and W be the dimensions of the expanded rectangle.\r\n" );
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document.write( "Then its perimeter is 2*(L+W),  hence L+W =  = 220 ft\r\n" );
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document.write( "and the average between L and W is   =  = 110 ft.\r\n" );
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document.write( "Since 110 ft is the average,  L = 110 + x  and  W = 110 - x,  where x is an unknown deviation.\r\n" );
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document.write( "Then  the area = 7200 = L*W = (110+x)*(110-x) = \r\n" );
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document.write( "which implies   = 12100 -7200 = 4900.\r\n" );
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document.write( "Hence, x =  = 70 ft.\r\n" );
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document.write( "Therefore,  L = 110 + 70 = 180  (I assume that L is the larger dimension !),  and the length of the original rectangle was/is 180/3 = 60 ft.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Did you noticed that I solved the problem MENTALLY ?\r
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\n" ); document.write( "\n" ); document.write( "2. Another mental solution\r
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document.write( "The area of 7200 ft^2 is the product of two numbers, whose sum is   = 220, as we saw in the Solution 1.\r\n" );
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document.write( "Try to find decomposition of the integer 7200 into the product of two factors that sum up to 220:\r\n" );
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document.write( "7200 = 10*720 = 20*360 = 30*240 = 40*180 . . .     ! O-o-o-ps ! That's it ! \r\n" );
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document.write( "So, you just found the length of the expanded rectangle.\r\n" );
document.write( "It is 180 ft.\r\n" );
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document.write( "Hence, the length of the original rectangle was   = 60 ft,\r\n" );
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document.write( "and you got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "3. Algebraic solution\r
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document.write( "You have \r\n" );
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document.write( "L + W = 220   (1)   and\r\n" );
document.write( "LW = 7200.    (2)\r\n" );
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document.write( "From (1), express  W = 220-W and substitute into (2). You will get\r\n" );
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document.write( "L*(220-L) = 7200,   or\r\n" );
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document.write( "L^2 - 220*L + 7200 = 0.\r\n" );
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document.write( "Solve this quadratic equation by any method you know.\r\n" );
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document.write( "For example, using factoring for the left side\r\n" );
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document.write( "(L-180)*(L-40) = 0.\r\n" );
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document.write( "Then for L (for the larger dimension) you obtain L = 180 ft.\r\n" );
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document.write( "Finally,  = 60 ft  is your answer to the problem's question.\r\n" );
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