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?
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