Identify Common Pythagorean Triples
A Pythagorean triple is a list of three numbers that fits the Pythagorean theorem — the square of the largest number is equal to the sum of the squares of the two smaller numbers. The multiple of any Pythagorean triple (multiply each of the numbers in the triple by the same positive number) is also a Pythagorean triple. They seem to reinvent themselves.
Familiarizing yourself with the more frequently used Pythagorean triples is very helpful. If you recognize that you have a triple, then working with applications is much easier.
The following table shows some of the most common Pythagorean triples and some of their multiples.
| Triple | Triple x 2 | Triple x 3 | Triple x 4 |
|---|---|---|---|
| 3, 4, 5 | 6, 8, 10 | 9, 12, 15 | 12, 16, 20 |
| 5, 12, 13 | 10, 24, 26 | 15, 36, 39 | 20, 48, 52 |
| 7, 24, 25 | 14, 48, 50 | 21, 72, 75 | 28, 96, 100 |
| 9, 40, 41 | 18, 80, 82 | 27, 120, 123 | 36, 160, 164 |
| 11, 60, 61 | 22, 120, 122 | 33, 180, 183 | 44, 240, 244 |
Here’s how to check out a triple by using the Pythagorean theorem. Try out the triple 9, 40, 41:
Replace a, b, and c with 9, 40, and 41, respectively.
Replace a, b, and c with the 9-40-41 triple multiplied by 3 (27, 120, 123).
