document.write( "Question 1103039: A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #717740 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
For a rectangle,
\n" ); document.write( " $\"A=L%2AW\"$
\n" ); document.write( "In this case,
\n" ); document.write( " $\"W%2BL%2BW=2400\"$
\n" ); document.write( " $\"2W%2BL=2400\"$
\n" ); document.write( " $\"L=2400-2W\"$
\n" ); document.write( "Substituting into the area equation,
\n" ); document.write( " $\"A=%282400-2W%29W\"$
\n" ); document.write( " $\"A=-2W%5E2%2B2400W\"$
\n" ); document.write( "Get the area into vertex form by completing the square to find the max area.
\n" ); document.write( " $\"A=-2%28W%5E2-1200W%2B600%5E2%29%2B2%28600%29%5E2\"$
\n" ); document.write( " $\"A=-2%28W-600%29%5E2%2B2%28360000%29\"$
\n" ); document.write( " $\"A=-2%28W-600%29%5E2%2B720000\"$
\n" ); document.write( "So the max area occurs when $\"W=600\"$ $\"ft\"$ and is equal to $\"720000\"$ $\"ft%5E2\"$
\n" ); document.write( "So then from above,
\n" ); document.write( " $\"A=L%2AW\"$
\n" ); document.write( " $\"L=720000%2F600\"$
\n" ); document.write( "Solve for L.
\n" ); document.write( " \n" ); document.write( "

\n" );