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.

right triangle

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

Let's see if you understand this concept.

If I want to create a Pythagorean Triple that is a multiple of 3 , 4 and 5

. . . and the first 2 numbers of the triple are  27 and 36 . . . what is the third number of the triple?