Final answer:
A Pythagorean Triple is a set of three positive integers that form the sides of a right-angled triangle and satisfy the equation a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13), and multiples of these sets are also Pythagorean Triples.
Step-by-step explanation:
A Pythagorean Triple consists of three positive integers a, b, and c, such that they form the sides of a right-angled triangle and satisfy the condition a² + b² = c², where c is the length of the hypotenuse (the side opposite the right angle), and a and b are the lengths of the other two sides.
This relationship is derived from the Pythagorean Theorem, which is a key principle in geometry and describes the relationship between the sides of any right-angled triangle.
Examples of Pythagorean Triples include the sets (3, 4, 5) and (5, 12, 13), as well as any other set of three numbers that fits the equation.
It's important to note that multiples of a Pythagorean Triple are also Pythagorean Triples; for example, (6, 8, 10) is a multiple of (3, 4, 5) and is also a Pythagorean Triple.