Since the perimeter is x + 2y and the total fence available is 500 m we write x + 2y = 500. From this, x is found as,

x=500-2y and the area of this rectengular is x.y=(500-2y).y = 500y-2y²

f(y)=500y-2y²

f'(y)=500-4y

f'(y)=500-4y=0 (for local maximum value)

y=125m and x=250 m

max area is x.y=125m*250m=31250 m²