Question

Find the pythagorean triplet whose smallest number is $12$

Answer 1

For every natural number $m>2,(2m,m^2-1,m^2+1)$ is a pythagorean triplet and the smallest number is $2m$

Given:$2m=12\Rightarrow m=\frac{12}{2}=6$

$\Rightarrow m^2-1=6^2-1=36-1=35$

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

$\therefore$ The triplet is $(12,35,37)$