Question

Triangle CDE is similar to triangle PQR. CD EQUALS 9m, EC EQUALS 15m PQ equals 15m. What is the length of RP

Answer 1

To find the length of \( RP \), we can use the property of similar triangles, which states that the ratios of corresponding sides of similar triangles are equal.

Given:
- Triangle \( CDE \) is similar to triangle \( PQR \).
- \( CE = 15m \)
- \( CD = 9m \)
- \( PQ = 15m \)

From the similarity of the triangles, we can set up the following proportion based on the corresponding sides \( CD \) and \( PQ \):

\[
\frac{CD}{PQ} = \frac{CE}{RP}
\]

Substituting the known values into the proportion:

\[
\frac{9}{15} = \frac{15}{RP}
\]

To solve for \( RP \), first cross-multiply:

\[
9 \cdot RP = 15 \cdot 15
\]

This simplifies to:

\[
9 \cdot RP = 225
\]

Now, dividing both sides by 9 gives:

\[
RP = \frac{225}{9}
\]
\[
RP = 25
\]

Thus, the length of \( RP \) is \( 25m \).