First use the material to find the restrictions on the variables...
m=2x+2y
y=(m-2x)/2
Now area is:
A=xy, and using y found above we have:
A=(mx-2x^2)/2
dA/dx=(m-4x)/2
d2A/dx2=-4/2=-2
Since acceleration is a constant negative value, when velocity, dy/dx=0, it is at the point of an absolute maximum for A(x)...
dA/dx=0 only when 4x=m, x=m/4
So this indicates that x=y=m/4.
Which means that the maximum possible area is when a perfect square is formed..
In this case m/4=20/4=5.
So the garden will be a perfect 5 foot square having an area of 25 ft^2.
