Question

Find the value of x in the figure below if RE is parallel to PM.

Answer 1

Answer:

Option C. 7.2 units

Step-by-step explanation:

we know that

triangle PAM is similar to triangle RAE by AA Similarity Theorem

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

$\frac{PA}{RA}=\frac{AM}{AE}$

substitute the given values

$\frac{20+x}{20}=\frac{25+9}{25}$

solve for x

$\frac{20+x}{20}=\frac{34}{25}$

$20+x=\frac{34}{25}(20)$

$x=\frac{34}{25}(20)-20$

$x=7.2\ units$