Recognizing Pythagorean Triples
You have already learned about the Pythagorean Theorem and how it helps you calculate the lengths of the sides of right triangles.
Sometimes it becomes useful to recognize integer outcomes (no decimals or fractions) of the Pythagorean Theorem. These special cases are called Pythagorean Triples and they turn up in your mathematics studies often.
Hopefully this is a Pythagorean Triple that you are familiar with;
3 , 4 , 5
You can make sure that it is a Pythagorean Triple by checking to see if it works in the Pythagorean Theorem.
3² + 4² = 5²
Yep; 9 + 16 = 25
It turns out that all multiples of 3, 4, and 5 work in the Pythagorean Theorem.
6, 8, and 10 Lets make sure. What is 6² + 8² equal to? 36 + 64 = 100
√100 should be the third side of the right triangle and that equals 10. So, 6, 8, and 10 are a Pythagorean Triple.
Here are some other triples that are multiples of the 3, 4, 5 triple.
9, 12, and 15
15, 20, and 25