Question

What the heck is a Pythagorean triple?

How can you tell if three positive numbers form a Pythagorean triple?

Answer 1

how can you tell if three positive numbers form a Pythagorean triple?

well here

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Answer 2

A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, if a, b, and c are the lengths of the sides of a right triangle such that c is the length of the hypotenuse, then a^2 + b^2 = c^2.

Examples of Pythagorean triples include (3,4,5), (5,12,13), and (8,15,17).

To tell if three positive numbers form a Pythagorean triple, you can use the Pythagorean theorem. If the sum of the squares of the two smaller numbers is equal to the square of the largest number, then the three numbers form a Pythagorean triple.

For example, suppose you have the numbers 6, 8, and 10. To check if they form a Pythagorean triple, you can calculate:

6^2 + 8^2 = 36 + 64 = 100
10^2 = 100

Since the two values are equal, the three numbers form a Pythagorean triple. In this case, the triple is (6,8,10), which satisfies the Pythagorean theorem:

6^2 + 8^2 = 10^2