Chapter 8, Problem 11RP

To determine

To calculate:The lengths of RP and OP segments of the given triangle.

Answer to Problem 11RP

The length of RP is 4 units and

The length of OP is 15 units

Explanation of Solution

Given information:

Given lengths of sides of triangles and given two sides are parallel

Formula used:

Comparing ratios of corresponding sides

Calculation :

In the triangles given,

  $\begin{array}{l}\frac{KR}{KM}=\frac{KP}{OK}\\ \Rightarrow \frac{8}{6}=\frac{KP}{9}\\ \Rightarrow KP=9\times \frac{8}{6}\\ \Rightarrow KP=12\text{ units}\\ \therefore \\ RP=KP-KR\\ RP=12-8\\ RP=4\text{ units}\end{array}$