and , since you only need one extra length to go down the middle. Since you want to minimise the cost of the fencing, you need to minimise the perimeter.
You know .
This is minimised when the derivative is 0, so
To be a minimum, the second derivative needs to be positive at that point.
So this is definitely the minimum.
So the dimensions are:
and , with as the length used to divide the paddock in half.