## Geometry: Common Core (15th Edition)

The Pythagorean Theorem states that for any right triangle, $a^{2} + b^{2} =c^{2},$ where c is the length of the hypotenuse and a and b are the length of the other two sides. Given that the numbers are natural numbers, we plug them into the Pythagorean Theorem to see if they are a Pythagorean Triple. (Note, the longest side is the hypotenuse.) $$32^2 + 60^2 = 68^2 \\ 1024 + 3600 = 4624 \\\\ 4624=4624$$ This is true, so it is a Pythagorean Triple.