By counting a set of dots in two different ways, give a combinatorial proof that
$$n^2 = 2{n \choose 2} + n$$
I read an example online saying that $n^2$ can be represented by a square set of dots, and ${n \choose 2}$ can be represented by a triangle with $n$ rows and $n-1$ columns. When you put two of these triangles together you get a rectangle that is given by $n \times n-1$ in dimensions and the final $+n$ makes up for the missing column making the two sides equal.
I was wondering if there was a better way to write this proof out or if this is a solid proof for the question.