Question

Find a Pythagorean triplet whose one number is $12$.

Answer 1

Find the Pythagorean triplets for the number $\mathbf{12}$:

Pythagorean triplets are in the form $\mathbf{2}\mathit{m}\mathbf{,}\mathbf{}{\mathit{m}}^{\mathbf{2}}\mathbf{-}\mathbf{1}$and ${\mathit{m}}^{\mathbf{2}}\mathbf{+}\mathbf{1}$.

It is given that one number is $12$ and $2m$ is even.

So,

$$\begin{gathered} 2m=12 \\ \Rightarrow m=6 \end{gathered}$$

Second Number is

$$\begin{gathered} m^2-1 \\ =6^2-1 \\ =35 \end{gathered}$$

And third number is

$$\begin{gathered} m^2+1 \\ =6^2+1 \\ =37 \end{gathered}$$

Hence, the Pythagorean triplet is $\mathbf{12}\mathbf{,}\mathbf{}\mathbf{35}$and $\mathbf{37}$.