document.write( "Question 1033564: A rancher has 216 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will produce the largest total area?
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Algebra.Com's Answer #648202 by ikleyn(52794) $\"\"$ $\"About$

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A rancher has 216 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will produce the largest total area?
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document.write( "I will assume that we have two adjacent rectangular corrals with the same dimensions L (length) and W (width), \r\n" );
document.write( "One common side (the length) is common for two corrals and the fence is installed along all sides, \r\n" );
document.write( "including the common interior side, although it is not stated directly in the condition.\r\n" );
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document.write( "If so, then we have this equation\r\n" );
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document.write( "3L + 4W = 216, \r\n" );
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document.write( "and we need to maximize the value f = L*2W.\r\n" );
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document.write( "Express 2W via L from (1): 2W = , and substitute it into L*2W. You will get \r\n" );
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document.write( "f =  = .\r\n" );
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document.write( "To maximize  means the same as to maximize . So, we can take off this multiplier .\r\n" );
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document.write( "Now we need to find the value of L which maximize this quadratic function\r\n" );
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document.write( "g(L) = L*(216-3L) = .\r\n" );
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document.write( "Those who know calculus can easily get the answer: L =  = 36 feet.\r\n" );
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document.write( "The others can determine the vertex of the parabola g(L) =  using formulas from algebra.\r\n" );
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document.write( "L =  =  =  = 36 feet and get the same answer.\r\n" );
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document.write( "Answer. The length of the corral should be 36 feet, the width of each corral is  =  = 27 feet.\r\n" );
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document.write( "        The total area of the two corrals is 2*36*27 = 1944 square feet.\r\n" );
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