Which of the following are pythagorean triples?

Second option

Step-by-step explanation: A pythagorean triple is a set of integers that satisfies the pythagorean theorem or a² + b² = c².  

The answer is the second option but let's understand why it's that choice.

3, 4, 5 is a pythagorean triple because (3)² + (4)² = (5)² or 9 + 16 = 25. This means that 3, 4, 5 is a pythagorean triple.

5, 12, 13 is a pythagorean triple because (5)² + (12)² = (13)² or 25 + 144 = 169. This means that 5, 12, 13 is a pythagorean triple.

8, 15, 17 is a pythagorean triple because (8)² + (15)² = (17)² or 64 + 225 = 289. This means that 8, 15, 17 is a pythagorean triple.

7, 24, 25 is a pythagorean triple because (7)² + (24)² = (25)² or 49 + 576 = 625. This means that 7, 24, 25 is a pythagorean triple.

Now, let's look at 1 from each of the other 3 rows and I'll explain why that one would not be a pythagorean triple.

2, 3, 4 would not be one because (2)² + (3)² ≠ (4)². In other words, 4 + 9 ≠ 16.

6, 8, 10 would not be one because (6)² + (8)² ≠ (10)². In other words, 36 + 64 ≠ 100.

9, 9, 9 would not be one because (9)² + (9)² ≠ (9)² or 81 + 81 ≠ 81.

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