△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP¯¯¯¯¯¯¯¯?(1 point)
Responses
25 m
25 m
0.6 m
0.6 m
30 m
30 m
9 m
9 m
To find the length of RP¯¯¯¯¯¯¯¯, we can use the concept of similarity. When two triangles are similar, their corresponding sides are proportional.
From the given information, we know that △CDE∼△PQR. This means that the ratio of the corresponding sides of the two triangles are equal.
In △CDE, CD=9 m and EC=15 m.
In △PQR, PQ=15 m.
To find RP¯¯¯¯¯¯¯¯, we can set up a proportion using the corresponding sides CD and PQ:
CD/PQ = DE/QR
Substituting the given values:
9/15 = DE/QR
Cross multiplying:
9QR = 15DE
Dividing both sides by 9:
QR = (15/9)DE
QR = (5/3)DE
Now, we need to find the value of DE. From the given information, CD=9 m and EC=15 m. Therefore, DE = 9 m + 15 m = 24 m.
Substituting this value into the proportion:
QR = (5/3)(24)
QR = 40
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 40 m.
The correct answer is: 40 m