Since the triangles △CDE and △PQR are similar (denoted as △CDE∼△PQR), their corresponding sides are in proportion. We know the following measurements:
- CD = 9 m
- EC = 15 m
- PQ = 15 m
Let RP be the side we want to find. Since the triangles are similar, we can set up a proportion based on their corresponding sides:
\[ \frac{CD}{PQ} = \frac{EC}{RP} \]
Substituting the known values:
\[ \frac{9 \text{ m}}{15 \text{ m}} = \frac{15 \text{ m}}{RP} \]
Now cross-multiply:
\[ 9 \cdot RP = 15 \cdot 15 \]
\[ 9 \cdot RP = 225 \]
Now, divide both sides by 9:
\[ RP = \frac{225}{9} = 25 \text{ m} \]
So, the length of \( RP \) is 25 m.