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