Pythagorean Triplets

There are a few common triangles that appear on the ACT math section that are called “Pythagorean Triplets”. These are right triangles where if a student knows two of the sides, they also can know the third side automatically without having to use the Pythagorean theorem. These triangles are known as 3,4,5 and 5-12-13 triangles.

The key for these triangles is to remember that the largest number has to be the hypotenuse for these to be true. So if a triangle has side lengths 5 and 13, but they are the two shorter sides, then it is not a 5-12-13 triangle.

These pythagorean triples remain true even when the numbers are scaled up by any given integer. So, when 3,4,5 becomes 6,8,10 (each original number multiplied by 2), it’s still a pythagorean triple. As long as the proportions remain consistent, the relationship remains true for these types of triangles.