Given that \(\triangle CDE \sim \triangle PQR\), the sides of the triangles are proportional.
You have the lengths:
- \(CD = 9\) m
- \(EC = 15\) m
- \(PQ = 15\) m
From this information, we can establish the ratios based on the similarity of the triangles.
First, find the length of \(CE\): \[ CE = CD + EC = 9 \text{ m} + 15 \text{ m} = 24 \text{ m} \]
Now we set up the ratio from the corresponding sides: \[ \frac{CD}{PQ} = \frac{CE}{RP} \] Substituting the values we know: \[ \frac{9}{15} = \frac{24}{RP} \]
Cross-multiply to solve for \(RP\): \[ 9 \cdot RP = 15 \cdot 24 \] \[ 9 \cdot RP = 360 \] \[ RP = \frac{360}{9} = 40 \text{ m} \]
Thus, the length of \(RP\) is \(40\) m.
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