document.write( "Question 203860: A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible? \n" ); document.write( "
Algebra.Com's Answer #153804 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible?
\n" ); document.write( ".
\n" ); document.write( "Let x = width
\n" ); document.write( "and y = length
\n" ); document.write( ".
\n" ); document.write( "Perimeter:
\n" ); document.write( "2x+y = 100
\n" ); document.write( "Solving for y:
\n" ); document.write( "y = 100-2x
\n" ); document.write( ".
\n" ); document.write( "Area = xy
\n" ); document.write( "Area = x(100-2x)
\n" ); document.write( "Area = 100x-2x^2
\n" ); document.write( "Area = -2x^2+100x
\n" ); document.write( ".
\n" ); document.write( "This is a parabola that opens downward -- therefore, finding the vertex gives you the maximum.
\n" ); document.write( "axis of symmetry = -b/(2a) = -100/(-4) = 25
\n" ); document.write( ".
\n" ); document.write( "Largest possible area then is:
\n" ); document.write( "Area = -2x^2+100x
\n" ); document.write( "Area = -2(25)^2+100(25)
\n" ); document.write( "Area = -1250+2500
\n" ); document.write( "Area = 1250 square meters
\n" ); document.write( " \n" ); document.write( "
\n" );