The one that is a Pythagorean theorem is the triangle with side lengths 5, 12, 13.

First, let's see if the triangle with side lengths 4, 5, 6 is a Pythagorean triple(The side lengths work for Pythagorean Theorem). We see that 6 is the hypotenuse because it's the greatest side. 4^{2}+5^{2} = 41, 41 is not 6^{2} which is 36. So the first option doesn't work

Next, let's see if 15, 6, 10 is a Pythagorean triple, we see again that 15 is our hypotenuse. 6^{2}+10^{2}= 136, 136 is not= 15^{2} so the second option doesn't

work.

Let's see if 12,8,10 works! 12 = hypotenuse, 8^{2}+10^{2}=164, 12^{2}=144 this means that the third option doesn't work which means the last one is the only option left, though I would memorize these common Pythagorean triples.

**The answer is the last option or the triangle with sides 5, 12, 13**

Please let me know if you have any questions.

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