To solve for the length of \( RP \) in triangles \( \triangle CDE \sim \triangle PQR \), we can use the property of similar triangles. The lengths of corresponding sides are proportional.
Given:
- \( CD = 9 , m \)
- \( EC = 15 , m \)
- \( PQ = 15 , m \)
Now, let's denote the corresponding side \( RP \).
From the similarity of triangles: \[ \frac{CD}{PQ} = \frac{EC}{RP} \]
Substituting in the known values: \[ \frac{9}{15} = \frac{15}{RP} \]
Cross-multiplying to solve for \( RP \): \[ 9 \cdot RP = 15 \cdot 15 \] \[ 9 \cdot RP = 225 \] \[ RP = \frac{225}{9} = 25 , m \]
Thus, the correct response is 25 m.