Find the Similarity Ratio: Comparing Triangles ΔGHF, ΔNOM and ΔABC in a Nested Structure

To solve this problem, we need to calculate the similarity ratio between $\Delta GH F$ and $\Delta ABC$. Since both triangles are equilateral:

• The side length of $\Delta ABC$ is $18$, and the side length of $\Delta GH F$ is $2$.
• The similarity ratio $\frac{\text{side of } \Delta ABC}{\text{side of } \Delta GHF}$ is:
\item $\frac{18}{2} = 9.$

Therefore, the similarity ratio between triangles $\Delta GHF$ and $\Delta ABC$ is $9$. The correct choice is:

$\frac{AB}{GF}=\frac{AC}{FH}=9$.