Check whether the following triplets are Pythagorean Triplets:- $( 5,\ 12,\ 13)$.

Given: Triplets $( 5,\ 12,\ 13)$.

To do: To check whether the given triplets are Pythagorean Triplets.

According to Pythagorean triplet:

The square of the largest number is equal to the sum of square of other two numbers.

Here, $13^2= 169$, $12^2=144$, $5^2=25$

$\therefore 12^2+5^2=144+25=169$

$\Rightarrow 13^2=12^2+5^2$

Hence they are Pythagorean triplet.