Learn About The Pythagorean Triples

In this video, we are going to look at Pythagorean Triples. From the previous video, we already know that the formula for the Pythagorean theorem is:
$a^2+b^2=c^2$

Many times in mathematics, we will often end up with decimal answers when solving for a missing side by applying the Pythagorean theorem. Pythagorean triples, however, are whole numbers.

Pythagorean Triples: Series of three whole numbers that make up sides of a right triangle

Only select integers are included in Pythagorean triples:
{3, 4, 5}
{5, 12, 13}
{8, 15, 17}

If we multiply each integer by other integers, we will arrive at other triples:
{3, 4, 5} $(\times2)=$ {6, 8, 10}
{3, 4, 5} $(\times3)=$ {9, 12, 15}
{5, 12, 13} $(\times2)=$ {10, 24 26}
{5, 12, 13} $(\times3)=$ {15, 36, 39}
{8, 15, 17} $(\times2)=$ {16, 30, 34}
{8, 15, 17} $(\times3)=$ {24, 45, 51}

Knowing these will save a lot of time by eliminating the need to use Pythagorean theorem every time.

Video-Lesson Transcript

Let’s go over Pythagorean triples.

We know that Pythagorean theorem is

$a^2 + b^2 = c^2$

where $a$ and $a$ are the legs and $c$ is the hypotenuse

Sometimes we’re doing Pythagorean theorem and searching for one of the sides and we end up a decimal answer. Only select integers work in here.

If we know that

$3^2 + 4^2 = 5^2$

But it would be different if we have different numbers.

$a^2 + b^2 = c^2$

$3^2 + 7^2 = c^2$

$9 + 49 = c^2$

$58 = c^2$

$\sqrt{58} = \sqrt{c^2}$

$7.6157731 = c$

Here, we did not get an integer answer.

We’ll only get an integer when we get a square root of a perfect square. Like square root of 49, square root of 64, square root of 144, all of those will give us an integer.

Pythagorean triples are a group of integers that work in this perfectly.

We’d like to list some of them:

{ $a, b, c$ }