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

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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 + 12 2 = 25 + 144

     = 169

     = 13 2

Thus, 5, 12, 13 are Pythagorean Triplets.

 

In General

(2m) + (m - 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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.