△CDE∼△PQR

Question

. 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

9 m
9 m

30 m
30 m

Answer 1

Given that $\mathrm{△}CDE\sim \mathrm{△}PQR$, the sides of the triangles are proportional.

From the information:

• $CD=9$ m
• $EC=15$ m
• $PQ=15$ m

Let $RP$ be denoted as $x$.

We can set up a proportion based on corresponding sides:

$$\frac{CD}{PQ}=\frac{EC}{RP}$$

Substituting the known values:

$$\frac{9}{15}=\frac{15}{x}$$

Cross-multiplying gives:

$$9x=15\times 15$$ $$9x=225$$ $$x=\frac{225}{9}=25$$

Thus, the length of $RP$ is $25$ m.

The answer is 25 m.