# List of Pythagorean triples

Three positive numbers a, b, and c make up a Pythagorean triple if their sum, a2 + b2, equals their sum, c2. A standard way to write such a triple is (a, b, c). One of the most common well-known example of Pythagorean triples is (3, 4, 5).

Complete List of Pythagorean Triples

Pythagorean triples are formed by positive integers a, b and c, such that a2 + b2 = c2. We may write the triple as (a, b, c).

For example, the numbers 3, 4 and 5 form a Pythagorean Triple because 32 + 42 = 52. There are infinitely many Pythagorean triples.

Some most commonly used triplets are:

### Pythagoras Theorem Examples and Questions

Example 1: ∆ ABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.

Refer to the figure given on the right.

As the triangle is right-angled, by Pythagoras theorem,
AB² = AC² + BC²

AB² = 5² + 12²
AB² = 25 + 144
AB² = 169 = 13²

Hence, AB = 13 cm

Example 2 : The side of a square is given to be 4 cm. Find the length of the diagonal of a square.

Solution: We need to find the length of the diagonal AC. As we know, all sides of a square are equal and each angle is 90 degrees, ADC is a right-angled triangle.

By Pythagoras theoram,