Sign In
A Pythagorean triple, commonly written as (a,b,c), is a set of three natural numbers that satisfy the Pythagorean Theorem. a^2+b^2=c^2 A right triangle can be drawn using the numbers of a Pythagorean triple as its side lengths. The lowest valued set of numbers that form a Pythagorean triple are 3, 4, and 5. There are infinitely many Pythagorean triples. The following table shows a few.
| Triple | Substitute in a^2+b^2=c^2 | Simplify |
|---|---|---|
| ( 3, 4, 5) | 3^2+ 4^2? = 5^2 | 9+16=25 ✓ |
| ( 5, 12, 13) | 5^2+ 12^2? = 13^2 | 25+144=169 ✓ |
| ( 8, 15, 17) | 8^2+ 15^2? = 17^2 | 64+225=289 ✓ |
| ( 7, 24, 25) | 7^2+ 24^2? = 25^2 | 49+576=625 ✓ |
If (a,b,c) is a Pythagorean triple, then so is (ka,kb,kc) for any natural number k.
| (a,b,c) | k | (ka,kb,kc) |
|---|---|---|
| ( 3, 4, 5) | 3 | ( 3( 3), 3( 4), 3( 5)) ⇕ (9,12,15) |
| ( 5, 12, 13) | 2 | ( 2( 5), 2( 12), 2( 13)) ⇕ (10,24,26) |