It seems like you're working with a geometric problem involving a triangle $\triangle ABC$ and a line segment $DE$ parallel to side $BC$. Based on the given information, let me first restate the problem more clearly:

• $B$ and $D$ are points on side $AB$.
• $C$ and $D$ are points on side $AC$.
• Line $DE$ is parallel to side $BC$.
• $AD = 2 \, \text{cm}$.
• $BD = 3 \, \text{cm}$.
• You're looking for the ratio $\frac{AC}{A}$, but it seems that the rest of this information is incomplete.

Could you please clarify or provide more details about the ratio you're asking for? For example, is it the ratio of $AC$ to $AB$, or some other specific ratio you're seeking? This would help me provide a complete solution.

Would you like me to assist with more details or follow-up questions?

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Here are five related questions to expand on this information:

1. Is there any information given about the length of $AC$?
2. Do you know the position of point $E$ on the line?
3. Are you using any specific triangle theorem like Thales' theorem or the intercept theorem?
4. Does the problem mention any angles between sides?
5. Is there any need to compute areas or other measurements related to triangle $ABC$?

Tip: In triangle problems with parallel lines, applying similarity of triangles can often simplify finding unknown lengths or ratios.