Chapter 6.9, Problem 24SR

To determine

To find: the value of $x$ .

Answer to Problem 24SR

The required value is $x=13.5$ .

Explanation of Solution

Given information:

Triangle $JMK$ is similar to triangle $PRO$ .

Calculation:

Consider Figure 1.

Triangle $JMK$ and triangle $PRO$ are similar.

  

Since $\Delta JMK\square \Delta PRO$

Therefore, their corresponding sides are proportional

  $\frac{JM}{PR}=\frac{JK}{PO}$

Substitute $JM=x,PR=9,JK=9,PO=6$ and simplify.

  $\begin{array}{c}\frac{JM}{PR}=\frac{JK}{PO}\\ \frac{x}{9}=\frac{9}{6}\\ 6x=9\times 9\text{Cross}\text{produts}\\ x=\frac{81}{6}\text{Divide}\text{by}\text{6}\\ x=13.5\text{Simplify}\end{array}$

Hence, the required value is $x=13.5$ .