A Pythagorean Triple is a set of three numbers that are related like this:
(The square of one of them) = (the square of another one) + ( the square of the third one)
If three numbers are related that way, then they can be the lengths of the sides of
a right triangle. If they're not, then they can't.
They're called a "Pythagorean Triple" because the ancient Greek mathematician Pythagoras
was the one who wrote the famous formula that describes the relationship among the
sides of every right triangle. That's his formula, up in the second line of this answer.
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Yes
They are Pythagorean triples
They are Pythagorean triples
The numbers of 3, 4 and 5 are an example of a Pythagorean triplet
Pythagoras was well known for the Pythagorean Theorem.