document.write( "Question 256030: The Maximum Garden Problem. A farmer has 230 ft
\n" ); document.write( "of fence to enclose a rectangular garden. What is the
\n" ); document.write( "largest garden area that can be enclosed with the 230 ft
\n" ); document.write( "of fence? Explain your work \n" ); document.write( "

Algebra.Com's Answer #188187 by drk(1908) $\"\"$ $\"About$

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We need two formulas:
\n" ); document.write( "(i) $\"P+=+2L+%2B+2W\"$
\n" ); document.write( "(ii) $\"A+=+LW\"$
\n" ); document.write( "We are told that the perimeter is 230, so (i) becomes
\n" ); document.write( "(iii) $\"230+=+2L+%2B+2W\"$
\n" ); document.write( "or
\n" ); document.write( "(iv) $\"115+=+L+%2B+W\"$
\n" ); document.write( "step 1 - solve (iv) for L and we get
\n" ); document.write( "(v) $\"L+=+115+-+W\"$
\n" ); document.write( "step 2 - substitute (v) into (ii) to get
\n" ); document.write( "(vi) $\"A+=+%28115-W%29%28W%29\"$
\n" ); document.write( "writing (vi) in vertex form, we get
\n" ); document.write( "(vii) $\"-1%28W-57.5%29%5E2+%2B+57.5%5E2\"$
\n" ); document.write( "So, when W = 57.5, L = 57.5 and the max area is 3306.25 ft sq. \n" ); document.write( "

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