document.write( "Question 622200: You have 332 feet of fencing to enclose a rectangular region. What is the maximum area? \n" ); document.write( "

Algebra.Com's Answer #391188 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"L\"$ = the length
\n" ); document.write( "Let $\"W\"$ = the width
\n" ); document.write( "Let $\"+A+\"$ = the area
\n" ); document.write( "The perimeter = $\"+2L+%2B+2W+\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"+2L+%2B+2W+=+332+\"$
\n" ); document.write( " $\"+2L+=+332+-+2W+\"$
\n" ); document.write( " $\"+L+=+166+-+W+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+A+=+L%2AW+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+A+=+%28+166+-+W+%29%2AW+\"$
\n" ); document.write( " $\"+A+=+-W%5E2+%2B+166W+\"$
\n" ); document.write( "When the form of the equation is
\n" ); document.write( " $\"+f%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "The maximum occurs at
\n" ); document.write( " $\"W+=++-b%2F%282a%29+\"$
\n" ); document.write( " $\"+a+=+-1+\"$
\n" ); document.write( " $\"+b+=+166+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+-166%2F%28-2%29+\"$
\n" ); document.write( " $\"W+=++83+\"$
\n" ); document.write( " $\"+L+=+166+-+W+\"$
\n" ); document.write( " $\"+L+=+83+\"$
\n" ); document.write( "The maximum area is
\n" ); document.write( " $\"+83%2A83+=+6889+\"$ ft2\r
\n" ); document.write( "\n" ); document.write( "
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