Chapter 7.5, Problem 8PPS

To determine

To find: The value of $x$ .

Answer to Problem 8PPS

9

Explanation of Solution

Given:

  

Kindly look at the labeled diagram:

  

In $\Delta KLM,\Delta XZY$ :

  $\begin{array}{l}\angle K\cong \angle X\\ \angle L\cong \angle Z\end{array}$

By $A-A$ similarity, the $\Delta KLM\sim \Delta XZY$ .

In two similar triangles, the ratio of their corresponding sides, medians are equal.

  $\begin{array}{l}\frac{KL}{ZX}=\frac{MP}{YQ}\\ \Rightarrow \frac{12}{28}=\frac{x}{21}\\ \Rightarrow x=9\end{array}$