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 + 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
3. Pythagoras Theorem

Pythagoras Theorem 