document.write( "Question 865856: what is the largest rectangular area that can be enclosed with 16 meters of fence? \n" ); document.write( "
Algebra.Com's Answer #521910 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
what is the largest rectangular area that can be enclosed with 16 meters of fence?
\n" ); document.write( "Let L = length
\n" ); document.write( "and W = width
\n" ); document.write( ".
\n" ); document.write( "2(L + W) = 16 (equation 1)
\n" ); document.write( "area = WL (equation 2)
\n" ); document.write( ".
\n" ); document.write( "Solve equation 1 for L:
\n" ); document.write( "2(L + W) = 16
\n" ); document.write( "(L + W) = 8
\n" ); document.write( "L = 8-W
\n" ); document.write( ".
\n" ); document.write( "Substitute above into equation 2:
\n" ); document.write( "area = W(8-W)
\n" ); document.write( "area = 8W-W^2
\n" ); document.write( "area = -W^2+8W
\n" ); document.write( "this is a quadratic (parabola) that opens downwards (from the negative coefficient associated with the W^2 term). This means the vertex is the Max.
\n" ); document.write( "max is at
\n" ); document.write( "W = -b/(2a)
\n" ); document.write( "W = -8/(2*(-1))
\n" ); document.write( "W = -8/(-2)
\n" ); document.write( "W = 4 meters (width)
\n" ); document.write( ".
\n" ); document.write( "L = 8-W = 8-4 = 4 meters (length)
\n" ); document.write( ".
\n" ); document.write( "Maximum area is
\n" ); document.write( "WL = 4*4 = 16 square meters\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );