Pythagorean Triples

Pythagorean triples are formed by whole numbers, so that a² + b² = c².

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

5, 12, 13

8, 15, 17

7, 24, 25

If we multiply each number of a Pythagorean triple by the same number, we form another Pythagorean triple. For example 6, 8, 10 is a Pythagorean triple because it is 2(3), 2(4), 2(5).

Memorising some common Pythagorean triples can helpful.

For example, if we see that the sides of a triangle form a Pythagorean triple then we know that it is a right triangle.

The following video gives some examples of Pythagorean triples.

Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem.

Example:

Find the value of x

Solution:

Check for Pythagorean triple:

Get the ratio of the two given sides:

12 : 20 = 3 : 5 ( divide by 4 )

From the ratio, we know that it is a Pythagorean triple.

So, x = 4 × 4 = 16 cm

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