Two partitions are necessary to divide the area into 3. The length of these partitions is 730 feet so assuming they're parallel to each other and to one side of the rectangle they each have a length of 365 feet. This will also be the length of one side of the area being partitioned. So we can find the other dimension: 12825/365=35.137 ft approx. The partitions are each 365 ft long, so their other side must be 35.137/3=11.712 feet, if they are the same size.
There is another possible answer if the partitions also have to enclose the area as well as subdivide it. In this case, 730 feet includes the perimeter of the area. If we call the large rectangular enclosure dimensions a and b, the perimeter of the enclosure is 2a+2b and we need to add to this two more lengths for the internal partitioning. So 2a+4b=730, or a+2b=365. We also know that ab=12825 sq ft, the area of the enclosure. Substitute a=365-2b in the area equation and we get (365-2b)b=12825. So 2b^2-365b+12825=0. This factorises into (2b-95)(b-135)=0. So b=47.5 or 135 feet and a=270 or 95 feet. This answer is the more likely, because the quadratic factorised into integer solutions.