△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP¯¯¯¯¯¯¯¯?

Answer 1

To find the length of RP¯¯¯¯¯¯¯¯, we need to first find the length of DE¯¯¯¯¯¯¯¯.

Since ∆CDE∼∆PQR, we can set up the following proportion:
CD/DE = PQ/QR
9/DE = 15/QR
9QR = 15DE
QR = 15/9 * DE
QR = 5/3 * DE

Now, we know that CD + DE = 15m. Given that CD = 9m, we can find that DE = 15 - 9 = 6m.

So, QR = 5/3 * 6 = 10m.

Since RP is the sum of QR and PR, and PQ = QR = 10m, PR = 15 - 10 = 5m.

Therefore, the length of RP¯¯¯¯¯¯¯¯ is 5m.