Given that △CDE is similar to △PQR (denoted as △CDE∼△PQR), we can set up a proportion based on the lengths of corresponding sides.
From the problem, we have:
- CD = 9 m
- EC = 15 m
- PQ = 15 m
First, we calculate the length of CE:
- CE = CD + EC = 9 m + 15 m = 24 m
Now we can establish the proportion: \[ \frac{CD}{PQ} = \frac{CE}{RP} \]
Substituting the values we have: \[ \frac{9}{15} = \frac{24}{RP} \]
Cross-multiplying gives: \[ 9 \cdot RP = 15 \cdot 24 \]
Calculating the right side: \[ 15 \cdot 24 = 360 \]
Now, substitute back into the equation: \[ 9 \cdot RP = 360 \]
Solving for RP: \[ RP = \frac{360}{9} = 40 \text{ m} \]
This length of RP (40 m) is not among the provided responses. Please double-check the initial data provided in the question to align with the values for the similarity proportions, or if the data has been stated correctly, as the options listed (0.6 m, 30 m, 25 m, 9 m) do not match with the calculated length RP.
7 answers