Pythagorean triplets

A Pythagorean Triplet has 3 numbers a, b, c

and

  a ² + b ² = c ²

Thus, we say that (a, b, c) are Pythagorean triplet

Note : This a, b, c are sides of a right triangle

The most common Pythagorean Triplets are

• 3, 4, 5
• 5, 12, 13
• 7, 24, 25
• 8, 15, 17
  
  

Let’s see how we check them

For Numbers 3, 4, 5

   3 ² + 4 ² = 9+16

        = 25

        = 5 ²    

        ∴ 3 ² +4 ² =5 ²  

Thus, 3, 4, 5 are Pythagoras Triplets.

For Number  5, 12, 13

  5 ²  + 12 ² = 25 + 144

     = 169

     = 13 ²

Thus, 5, 12, 13 are Pythagorean Triplets.

In General

(2m) ²  + (m ²  - 1) ² = (m ² + 1) ²

Here,

  First number = 2m

  Second number = m ² - 1

  Third number = m ² + 1

from Pythagoras Triplets.

Note:

If we know that 3, 4, 5 are Pythagorean Triplets

Then,

3 × 2 = 6

4 × 2 = 8

5 × 2 = 10

So, (6, 8, 10) will also be a Pythagorean Triplet

Similarly, if we multiply by 3

(9, 12, 15) is also a Pythagorean Triplet

And, more generally, if we multiply by any number k

(3k, 4k, 5k) will also be a Pythagorean Triplet