document.write( "Question 1065428: A field must be fenced in. There is 212 yards of fencing material to be used. What should the dimensions of the enclosed area be to ensure that it has the largest possible area? \n" ); document.write( "

Algebra.Com's Answer #680597 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+W+\"$ = the width
\n" ); document.write( "Let $\"+L+\"$ = the length
\n" ); document.write( "Using formula for perimeter:
\n" ); document.write( " $\"+2W+%2B+2L+=+212+\"$
\n" ); document.write( " $\"+W+%2B+L+=+106+\"$
\n" ); document.write( " $\"+L+=+106+-+W+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "Let $\"+A+\"$ = the area
\n" ); document.write( " $\"+A+=+W%2A%28+106+-+W+%29+\"$
\n" ); document.write( " $\"+A+=+-W%5E2+%2B+106W+\"$
\n" ); document.write( "This is a parabola with the vertex a maximum,
\n" ); document.write( "and not a minimum
\n" ); document.write( "---------------------
\n" ); document.write( "Formula for vertex:
\n" ); document.write( " $\"+W%5Bv%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+a+=+-1+\"$
\n" ); document.write( " $\"+b+=+106+\"$
\n" ); document.write( " $\"+W%5Bv%5D+=+-106%2F%28+2%2A%28-1%29%29+\"$
\n" ); document.write( " $\"+W%5Bv%5D+=+53+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+L%5Bv%5D+=+106+-+W+\"$
\n" ); document.write( " $\"+L%5Bv%5D+=+106+-+53+\"$
\n" ); document.write( " $\"+L%5Bv%5D+=++53+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "The enclosed area is maximum when it is 53 yds x 53 yds
\n" ); document.write( "check:
\n" ); document.write( " $\"+4%2A53+=+212+\"$ yds of fencing
\n" ); document.write( "OK
\n" ); document.write( "Here's a plot of $\"+A+\"$ and $\"+W+\"$
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-15%2C+150%2C+-350%2C+3500%2C+-x%5E2+%2B+106x+%29+\"$
\n" ); document.write( " \n" ); document.write( "

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