which set reprosents a pythagoren triplels
To find a set that represents a Pythagorean triple, we need to find three positive integers (a, b, c) that satisfy the Pythagorean theorem, which 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.
The Pythagorean triple sets can be represented as (a, b, c), where a, b, and c are positive integers, and c is the hypotenuse. Therefore, we have three conditions that the set must satisfy:
1. a^2 + b^2 = c^2
2. a < c and b < c
3. a, b, and c are positive integers
Here are a few examples of Pythagorean triple sets:
1. (3, 4, 5):
- a = 3, b = 4, c = 5
- Verify: 3^2 + 4^2 = 9 + 16 = 25 = 5^2
2. (5, 12, 13):
- a = 5, b = 12, c = 13
- Verify: 5^2 + 12^2 = 25 + 144 = 169 = 13^2
3. (8, 15, 17):
- a = 8, b = 15, c = 17
- Verify: 8^2 + 15^2 = 64 + 225 = 289 = 17^2
These are just a few examples, and there are infinitely many Pythagorean triple sets. They can be generated using various methods, such as the Euclidean formula or by multiplying a simpler set by a common factor.