1. The problem asks which proportion can be used to find the value of $x$ given the side lengths of two hexagons. 2. The key idea is that corresponding sides of similar figures are proportional. Here, the small hexagon has sides $x$ and $0.5$ m, and the large hexagon has sides $0.7$ m and $2$ m. 3. To set up a proportion, match corresponding sides: $\frac{x}{0.5} = \frac{2}{0.7}$ or $\frac{0.5}{x} = \frac{0.7}{2}$ depending on which sides correspond. 4. Since $x$ corresponds to $2$ m and $0.5$ m corresponds to $0.7$ m, the correct proportion is: $$\frac{x}{0.5} = \frac{2}{0.7}$$ 5. This proportion relates the unknown side $x$ to the known side $0.5$ m in the small hexagon, and the corresponding sides $2$ m and $0.7$ m in the large hexagon. 6. Therefore, the correct answer is $\boxed{\frac{x}{0.5} = \frac{2}{0.7}}$.