Algebra.Com's Answer #666729 by ikleyn(52800)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible
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document.write( "enclosed area given 600 feet of fencing. (Assume that the length is greater than or equal to the width.)
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document.write( "I prepared the Figure on the right to show how I see and understand \r\n" );
document.write( "the condition.\r\n" );
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document.write( "In the Figure, L means the length and W means the width of each pen.\r\n" );
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document.write( "So, we have 3 pieces of fencing of the length L each and 4 pieces \r\n" );
document.write( "of fencing of the length W each.\r\n" );
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document.write( "Then we have this equation \r\n" );
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document.write( "3L + 4W = 600,\r\n" );
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document.write( "from which we have W =  .\r\n" );
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document.write( " Figure. \r\n" );
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document.write( " Next, the combined area of the two corals is \r\n" );
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document.write( "A = L*2W =  =  =  ,\r\n" );
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document.write( "and we have to find the length L in a way to maximize the area A, i.e. maximize the quadratic function\r\n" );
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document.write( "A =  .\r\n" );
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document.write( " Now let me remind you that, if you have a quadratic function f(x) =  of the general form, \r\n" );
document.write( " then it reaches the maximum/minimum at x =  .\r\n" );
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document.write( "For our situation, a =  and b = 300.\r\n" );
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document.write( "Therefore, the maximum is at L = -  =  = 100.\r\n" );
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document.write( "Thus the area get a maximum at L = 100 feet.\r\n" );
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document.write( "Then W = =  = 75 feet.\r\n" );
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document.write( "Answer. The area is maximal at L = 100 feet and W = 75 feet.\r\n" );
document.write( " Then the area of one coral is 100*75 = 7500 square feet.\r\n" );
document.write( " The combined area of the two corals is twice this value, i.e. 15000 square feet.\r\n" );
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document.write( " The plot below confirms this solution.\r
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document.write( "Plot f(L) = \r
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