document.write( "Question 1044337: Find the Maximum rectangular area that can be enclosed by a fence that is 224 m. Show your solution \n" ); document.write( "

Algebra.Com's Answer #659641 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the Maximum rectangular area that can be enclosed by a fence that is 224 m. Show your solution
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document.write( "Let x be the length of the rectangle and y be its width.\r\n" );
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document.write( "Then  x + y =  = 112,  and you are asked to find  x  and  y  in a way \r\n" );
document.write( "to maximize the product  x*y  which is the area.\r\n" );
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document.write( "Express  y  via  x:  y = 112 - x,  and substitute it into the product:\r\n" );
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document.write( "x*y = x*(112-x).\r\n" );
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document.write( "Now find the maximum of the quadratic function  f(x) = x*(112-x) = .\r\n" );
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document.write( "The maximum is the vertex at x = :\r\n" );
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document.write( "x =  = 56.\r\n" );
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document.write( "So, x = 56 feet. Then y = 112-x = 56 feet too, and the rectangle is actually a square.\r\n" );
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