document.write( "Question 872829: A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the maximum possible area of the field and the field's dimensions. \n" ); document.write( "
Algebra.Com's Answer #526448 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the maximum possible area of the field and the field's dimensions.
\n" ); document.write( ".
\n" ); document.write( "Let x = width
\n" ); document.write( "and y = length
\n" ); document.write( "2x+y = 400 (eq 1)
\n" ); document.write( "xy= area (eq 2)
\n" ); document.write( ".
\n" ); document.write( "Solving eq 1 for y:
\n" ); document.write( "y = 400-2x
\n" ); document.write( "substitute into eq 2
\n" ); document.write( "x(400-2x) = area
\n" ); document.write( "-2x^2+400x = area
\n" ); document.write( "since the above is a parabola that opens downwards, the vertex is the max.
\n" ); document.write( "x-value of the max is:
\n" ); document.write( "x = -b/(2a)
\n" ); document.write( "x = -400/(2(-2))
\n" ); document.write( "x = -400/(-4)
\n" ); document.write( "x = 100 feet (width)
\n" ); document.write( ".
\n" ); document.write( "length is:
\n" ); document.write( "2x+y=400
\n" ); document.write( "2(100)+y=400
\n" ); document.write( "200+y=400
\n" ); document.write( "y = 200 feet
\n" ); document.write( ".
\n" ); document.write( "Max area is:100*200 = 20000 square feet \n" ); document.write( "
\n" );