If one fenced side is length x, the other fenced side will be 100-x.
The area A=x(100-x)=100x-x².
A=100x-x²,
A=2500-2500+100x-x²,
A=2500-(2500-100x+x²),
A=2500-(50-x)².
This has a maximum value when x=50m and the area is 2500m².
So the area is square with side 50m.