Chapter 8, Problem 29RP

To determine

To find:The given segments in a given triangle i.e. QP, RS, and QS.

Answer to Problem 29RP

The lengths of required segments: QP = 8 units; RS = 6 units and QS = 8 units

Explanation of Solution

Given information:

One given ray $\overrightarrow{TQ}$ bisects the angle $\angle RTP$

Formula used:

Corresponding sides are equivalent

Calculation :

  $\begin{array}{l}\frac{QP}{PT}=\frac{RQ}{RT}\\ \Rightarrow \frac{QP}{28}=\frac{6}{21}\Rightarrow QP=8\text{ units}\\ \frac{RS}{PT}=\frac{RT}{RQ}\\ \Rightarrow \frac{RS}{8}=\frac{21}{28}\Rightarrow RS=6\text{ units}\\ \frac{QS}{PT}=\frac{RT}{RQ}\\ \Rightarrow \frac{QS}{6}=\frac{28}{21}\Rightarrow QP=8\text{ units}\end{array}$