document.write( "Question 335951: A farmer has 1000 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enlosed by the fence? \n" ); document.write( "

Algebra.Com's Answer #241356 by Fombitz(32388) $\"\"$ $\"About$

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The perimeter of the rectangle is,
\n" ); document.write( " $\"P=2L%2B2W=1000\"$
\n" ); document.write( " $\"L%2BW=500\"$
\n" ); document.write( "The area of a rectangle is,
\n" ); document.write( " $\"A=L%2AW\"$
\n" ); document.write( "From the perimeter equation,
\n" ); document.write( " $\"L=500-W\"$
\n" ); document.write( " $\"A=%28500-W%29W=500W-W%5E2\"$
\n" ); document.write( "Convert the area function to vertex form ( $\"y=a%28x-h%29%5E2%2Bk\"$ )to get the maximum value, which occurs at the vertex ( $\"h\"$ , $\"k\"$ ).
\n" ); document.write( " $\"A%28W%29=500W-W%5E2=-%28W%5E2-500W%29\"$
\n" ); document.write( " $\"A%28W%29=-%28W%5E2-500W%2B62500%29%2B62500\"$
\n" ); document.write( " $\"A%28W%29=-%28W-250%29%5E2%2B62500\"$
\n" ); document.write( "The maximum area occurs when $\"W=250\"$ ft and is equal to $\"A=62500\"$ .
\n" ); document.write( " $\"L=500-250\"$
\n" ); document.write( " $\"L=250\"$ ft
\n" ); document.write( "The maximum area for a given perimeter is a square.
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