# Pythagorean Triples

How to solve the Pythagorean triple problems: commonly used triples, examples, and their solutions.

## Triples

Pythagorean Triples are three positive integers

that satisfy the Pythagoran theorem: *a*^{2} + *b*^{2} = *c*^{2}.

Commonly used triples:

(3, 4, 5)

(5, 12, 13)

(7, 24, 25)

## Example 1

For the right triangle,

the leg is 4,

and the hypotenuse is 5.

Then the related triple is (3, 4, 5).

So *x* = 3.

## Example 2

For the right triangle,

the legs are 5 and 12.

Then the related triple is (5, 12, 13).

So *x* = 13.

## Example 3

For the right triangle,

the leg is 6,

and the hypotenuse is 10.

Then the related triple is (3, 4, 5),

because the given triangle

is similar to (3, 4, 5) triangle.

To find the scale (× 2) clearly,

draw the (3, 4, 5) triangle

next to the given triangle.

So *x* = 2⋅4 = 8.