△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP¯¯¯¯¯¯¯¯?(1 point)
Responses
0.6 m
9 m
30 m
25 m
To solve this problem, we can set up a proportion using the corresponding side lengths of the similar triangles.
Let RP = x m.
Using the side length ratios, we have the proportion:
CD/EC = PQ/RP
Substituting the given values, we get:
9/15 = 15/x
Cross multiplying, we have:
9x = 15 * 15
9x = 225
Dividing both sides by 9, we find:
x = 225/9
Simplifying, we get:
x = 25
So, the length of RP is 25 m. Therefore, the correct answer is 25 m.
To find the length of RP¯¯¯¯¯¯¯¯, we can use the property of similar triangles. Since △CDE∼△PQR, the corresponding sides are in proportion.
Let's set up the proportion using the corresponding sides:
CD / PQ = DE / QR
Substitute the given values CD=9m, EC=15m, and PQ=15m:
9 / 15 = DE / QR
To find the length of DE, we need to subtract EC from CD:
DE = CD - EC
DE = 9 - 15
DE = -6
Now, substitute the values into the proportion:
9 / 15 = -6 / QR
To solve for QR, we can cross-multiply:
9 * QR = 15 * -6
9QR = -90
Divide both sides by 9 to isolate QR:
QR = -90 / 9
QR = -10
The length of RP¯¯¯¯¯¯¯¯ is equal to QR, so the length of RP¯¯¯¯¯¯¯¯ is 10 m.