let z represent the other side of the rectangular plot

A rectangular plot requires 200 meters of railings to enclose it means that the perimeter of the rectangular plot is 200 meters:

2(x + z) = 200 divide both sides by 2

x + z = 100

z = 100 - x

The area of the rectangle is equal to the product of its sides thus:

y = x*z

plug z = 100 - x into the last equation

y = x(100 - x)

y = 100x - x^2 is the equation of the area as a function of x

since the length of the sides can not be negative numbers we have

x > 0

100 - x > 0

that is the domain is:

x > 0

x < 100

the domain is the interval (0, 100).