The dominions of a
certain Eastern monarch formed
tract of country.
It happened that the king one day discovered that his
four sons were not only plotting against each other, but were in secret
rebellion against himself. After consulting with his advisers he
not to exile the princes, but to confine them to the four corners of
country, where each should be given a triangular territory of equal
beyond the boundaries of which they would pass at the cost of their
Now, the royal
surveyor found himself confronted
difficulties, owing to the wild character of the country.
that while each was given exactly the same area, the four triangular
districts were all of different shapes, somewhat in the manner shown in
The puzzle is to
give the three measurements for
of the four districts in the smallest possible numbers—all
In other words, it is required to find (in the smallest
possible numbers) four rational right-angled triangles of equal area.