Triangle Height Problem: Finding Perpendicular Distance of 24 Units

To solve this problem, let's follow these steps:

• Step 1: Identify similar triangles and related segments.
• Step 2: Apply proportions based on geometric similarity principles.
• Step 3: Compare with the given options.

Let's work through each step:

Step 1: From the geometry, consider triangles and line segments such as $AD$, $AF$, and $AB$. These segments often form part of similar triangles with known properties.

Step 2: Based on triangle similarity properties, the ratio for segments in similar figures should follow a coherent pattern like that of proportions described for viable geometric figures, namely: $\frac{AD}{AF} = \frac{AF}{AB}$ This indicates the relationship of subsegments generated by these points. Use triangle proportionality theorem or similar property for derivation.

Step 3: Match this with the answer selections provided. The choice: $\frac{AD}{AF} = \frac{AF}{AB}$ corresponds directly with option 3 among the provided choices.

Therefore, the correct answer is: $\frac{AD}{AF}=\frac{AF}{AB}$.