Explanation:
We assume your question is "why is that name given to these three numbers?"
There are many names in mathematics that are given to sequences or sets of numbers having a particular characteristic. The term "Pythagorean triple" is usually reserved for three positive integers that satisfy the relation "the sum of the squares of the smaller two is equal to the square of the largest."
This relationship exists between the side lengths of a right triangle, which is the point of the Pythagorean theorem. So, integer side lengths of a right triangle constitute a "Pythagorean triple."
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If your question is "why do right triangle side lengths have the relationship specified by the Pythagorean theorem?", that demands a different answer. In general, the sides and angles of a triangle obey the Law of Sines and the Law of Cosines.
One of the expressions of the Law of Cosines is ...
c² = a² +b² -2ab·cos(C)
where C is the angle opposite side c in the triangle. You may recall that the cosine of 90° is zero, so the cosine term in this equation vanishes when angle C is a right angle. The remaining equation is ...
c² = a² +b²
This is an expression of the Pythagorean theorem, and it is true only for right triangles.
