can you give me at least 5 pythagorean triple theorem equations please
Certainly! The Pythagorean triple theorem states that in a right-angled 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 other two sides. Here are five examples of Pythagorean triples:
1) (3, 4, 5): This is one of the most well-known Pythagorean triples, where 3² + 4² = 5² (9 + 16 = 25).
2) (5, 12, 13): Another common Pythagorean triple, where 5² + 12² = 13² (25 + 144 = 169).
3) (8, 15, 17): Yet another Pythagorean triple, where 8² + 15² = 17² (64 + 225 = 289).
4) (7, 24, 25): This triple satisfies the theorem as well, where 7² + 24² = 25² (49 + 576 = 625).
5) (9, 40, 41): One more example of a Pythagorean triple, where 9² + 40² = 41² (81 + 1600 = 1681).
These are just a few examples, but there are infinitely many Pythagorean triples that can be generated by multiplying each of these triples by any positive integer.