# Pythagorean Triple

How to find the side of a right triangle by using the Pythagorean triple: definition, 3 examples, and their solutions.

## Definition

### Definition

The Pythagorean triple is three positive integers
that satisfy the Pythagorean theorem:
a2 + b2 = c2.

Below triples are the commonly used triples.

(3, 4, 5)
32 + 42 = 52

(5, 12, 13)
52 + 122 = 132

(7, 24, 25)
72 + 242 = 252

## Example 1

### Solution

The sides of the given right triangle are
(x, 4, 5).

The related triple is
(3, 4, 5).

So x = 3.

So x = 3 is the answer.

## Example 2

### Solution

The sides of the given right triangle are
(5, 12, x).

The related triple is
(5, 12, 13).

So x = 13.

So x = 13 is the answer.

## Example 3

### Solution

The sides of the given right triangle are
(6, x, 10).

(6, x, 10) looks like the multiple of (3, 4, 5).

So draw a (3, 4, 5) right triangle.

These two triangles are similar.

Then their sides are proportional.

So x/4 = 6/3.

Similar Triangles

6/3 = 2

x/4 = 2

Multiply 4 to both sides.

Then x = 8.

So x = 8.