A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$. What is the length of the side of the square (in $mm$) such that the combined area of the square and the rectangle is a $\textbf{MINIMUM}$?
- $30$
- $40$
- $120$
- $180$