Question

Find a Pythagorean triplet where one of the numbers is 12.

Answer 1

Pythagoras triplets are of the form $2m,m^2-1\text{and}{m}^2+1$
If we take $m^2–1=12$

$m^2=12+1=13$

Then the value of m will not be an integer.

So, we try to take, $m^2+1=12$

$m^2=12–1=11$

Again, the value of m will not be an integer.

So, let us take 2m = 12

$m=6$ which is an integer.

Thus, the other members of Pythagorean triplet are as follows :

$m^2–1=6^2–1=36–1=35$

$m^2+1=6^2+1=36+1=37$

Thus, the required triplet is 12, 35 and 37.