Scalenia is a country bounded by three straight frontiers called A, B, and C, of course, each of a different length but each an exact number of kilometers long.

The curious thing is that the length of A+B+C, and the lengths of A+B-C, A+C-B, and B+C-A, are all precisely square numbers of kilometers.

If Scalenia has the smallest perimeter consistent with this curious fact, what is the length of each of its frontiers?