△CDE∼△PQR . CD=9 m , EC=15 m , PQ=15 m . What is the length of RP¯¯¯¯¯¯¯¯ ?(1 point)
Responses
a)30 m
b)9 m
c)25 m
d)0.6 m
To find the length of RP¯¯¯¯¯¯¯¯, we need to determine the ratio of corresponding sides in similar triangles.
The given triangles are similar, so we can set up the following proportion: CD/PQ = DE/QR
Plugging in the given lengths, we have:
9/15 = DE/QR
Simplifying the fraction, we get:
3/5 = DE/QR
Cross multiplying, we get:
5(DE) = 3(QR)
Now, we need to find DE. We know that CD + DE = CE, so we can calculate DE:
DE = CE - CD
DE = 15 m - 9 m
DE = 6 m
Plugging this into our equation, we have:
5(6) = 3(QR)
30 = 3(QR)
QR = 30/3
QR = 10 m
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 10 m.
The correct answer is:
d) 10 m
wrong
Apologies for the error.
Let's try to solve it again.
We have ∆CDE ∼ ∆PQR. CD = 9 m, EC = 15 m, and PQ = 15 m.
To find the length of RP¯¯¯¯¯¯¯¯, we can set up the following proportion:
CD/EC = PQ/RP
Plugging in the given values, we have:
9/15 = 15/RP
Simplifying the fraction, we get:
3/5 = 15/RP
To solve for RP, we can cross multiply:
3(RP) = 5 * 15
3(RP) = 75
RP = 75/3
RP = 25 m
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 25 m.
The correct answer is:
c) 25 m