Question

Write a Pythagorean triplet whose one number is (i) 18 (ii) 6 (iii) 22

Answer 1

Answer:

(i) 18 , 80 , 82

(ii) 6 , 8 , 10

(iii) 22 , 120 , 122

Solution:

★ Note : Pythagorean triplet is given as;

2m , (m² - 1) , (m² + 1)

(i) Using 18 :-

We have ;

=> 2m = 18

=> m = 18/2

=> m = 9

Thus,

m² - 1 = 9² - 1 = 81 - 1 = 80

Also,

m² + 1 = 9² + 1 = 81 + 1 = 82

Hence,

The required Pythagorean triplet is :

18 , 80 , 82 .

(ii) Using 6 :-

We have ;

=> 2m = 6

=> m = 6/2

=> m = 3

Thus,

m² - 1 = 3² - 1 = 9 - 1 = 8

Also,

m² + 1 = 3² + 1 = 9 + 1 = 10

Hence,

The required Pythagorean triplet is :

6 , 8 , 10.

(iii) Using 22 :-

We have ;

=> 2m = 22

=> m = 22/2

=> m = 11

Thus,

m² - 1 = 11² - 1 = 121 - 1 = 120

Also,

m² + 1 = 11² + 1 = 121 + 1 = 122

Hence,

The required Pythagorean triplet is :

22 , 120 , 122 .