Question

If the largest member of the Pythagorean triplet is given to be $17$, then find the other two members of the Pythagorean triplet.

• A. $15,16$
• B. $8,15$
• C. $8,16$
• D. $7,8$

Answer 1

The correct option is B $8,15$

The three numbers that will form a Pythagorean triplet will be given as: $2m,m^2-1$, and $m^2+1$, where $m$ is any positive integer.

Here, the largest member of the Pythagorean triplet is $m^2+1$ and the smallest member is $2m$.

The three members of Pythagorean triplet can be represented as follows:


It is given that the largest side of the Pythagorean triplet is $17$.

$\begin{array}{cc}\therefore m^2+1& =17\\ m^2& =17-1\\ m^2& =16\\ m& =\pm 4\end{array}$

Since $m$ is a positive integer, therefore $m=4$.

Hence, the smallest member of the Pythagorean triplet is calculated as,

$\begin{array}{cc}\text{Smallest member of the triplet}& =2m\\ & =2\left(4\right)\\ & =8\end{array}$

Furthermore, the last member of the triplet is

$\begin{array}{cc}{m}^2-1& =4^2-1\\ & =16-1\\ & =15\end{array}$

Thus, the three members of Pythagorean triplet are $(8,15,17)$ and can be represented as,


Hence, the other two members of the Pythagorean triplet are $8$ and $15$.