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 + 4 = 9 + 16

           = 25

           = 5  

        ∴ 3 + 4 = 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.

 

For Numbers 7 , 24, 25

   3 2 + 4 2 = 9 + 16

           = 25

           = 5 2    

∴ 3 + 4 = 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) 2 + (m 2 - 1) 2 = (m 2 + 1) 2

 

Here,

  First number = 2m

  Second number = 2m

  Third number = m + 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

 

  1. Chapter 6 Class 7 Triangle and its Properties
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.