Question

What are Pythagorean Triplets?

Answer 1

Pythagorean triplet

Definition:

Pythagorean triplets are represented as $\left(a,b,c\right)$ such that $a^2+b^2=c^2$, where $a,b$ and $c$ are positive integers.

Here $a$ is the perpendicular, $b$ is the base and $c$ is the hypotenuse of the right angled triangle.

Example:

Consider $\left(5,12,13\right)$

Where,

$$\begin{gathered} a=5 \\ b=12 \\ c=13 \end{gathered}$$

Put $a=5,b=12\mathrm{and}c=13$ in $a^2+b^2=c^2$:

$\begin{array}{rcl}\mathrm{LHS}& =& a^2+b^2\\ & =& 5^2+{12}^2\\ & =& 25+144\\ & =& 169\\ & =& {13}^2\\ & =& c^2\\ & =& \mathrm{RHS}\end{array}$

Thus,$\left(5,12,13\right)$ satisfies $a^2+b^2=c^2$

Hence, Pythagorean triplets $\left(a,b,c\right)$ are sides of a right-angle triangle such that $a^2+b^2=c^2$, where $a,b$ and $c$ are positive integers and are perpendicular, base and hypotenuse respectively.