Given that \( \triangle CDE \sim \triangle PQR \), the sides of the triangles are proportional.
From the information:
- \( CD = 9 \) m
- \( EC = 15 \) m
- \( PQ = 15 \) m
Let \( RP \) be denoted as \( x \).
We can set up a proportion based on corresponding sides:
\[ \frac{CD}{PQ} = \frac{EC}{RP} \]
Substituting the known values:
\[ \frac{9}{15} = \frac{15}{x} \]
Cross-multiplying gives:
\[ 9x = 15 \times 15 \] \[ 9x = 225 \] \[ x = \frac{225}{9} = 25 \]
Thus, the length of \( RP \) is \( 25 \) m.
The answer is 25 m.