document.write( "Question 1134826: A rectangle has a length of 12 meters less than 2 times its width. If the area of the rectangle is 2574
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Algebra.Com's Answer #752351 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "W is the width;  (2W-12) is the length.\r\n" );
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document.write( "The area equation is\r\n" );
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document.write( "    W*(2W-12) = 2574.       (1)\r\n" );
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document.write( "Multiply both sides by 2 to get\r\n" );
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document.write( "    2W*(2W-12) = 5148.      (2)\r\n" );
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document.write( "Let x be the value midway between  2W  and  (2W-12)    (the arithmetic mean of the two expressions).\r\n" );
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document.write( "Then it is clear that  2W = x+6,  while  2W-12 = x-6.\r\n" );
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document.write( "Then the equation (2) becomes\r\n" );
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document.write( "    (x+6)*(x-6) = 5148\r\n" );
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document.write( "    x^2 - 36 = 5148\r\n" );
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document.write( "    x^2 = 5148 + 36 = 5184  ============>  x = \"sqrt%285184%29\" = 72.\r\n" );
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document.write( "Then  2W = x+6 = 72 + 6 = 78,  hence,  W = 78/2 = 39   and   L = 2W-12 = 2*39 - 12 = 66.\r\n" );
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document.write( "Answer.  The length of the rectangle is 66 meters.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that the only \"time consuming\" step in my solution was to take the square root of 5184.   //   Ha-ha-ha.\r
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document.write( "    (The rest can be done MENTALLY).\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see how this method/idea works in other similar problems, look into the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - Three methods to find the dimensions of a rectangle when its perimeter and the area are given\r
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\n" ); document.write( "\n" ); document.write( "Let me make my comment regarding the words by @greenestamps \"there is no advantage to using formal algebra\".\r
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document.write( "    All what we teach you in this site, is formal algebra and/or is based on formal algebra methods.\r\n" );
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document.write( "          Thanks to those intellectual giants who built this base . . . \r\n" );
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document.write( "    If sometimes we tell you about possibilities to solve the problems mentally, it is not to convince you do not use formal algebra.\r\n" );
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document.write( "    We do it only to wider your horizon and/or to make your mind more flexible.\r\n" );
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document.write( "    So, do not consider these words by the esteem tutor @greenestamps too seriously . . . \r\n" );
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document.write( "    Consider them in a \"joking mode\" . . . \r\n" );
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