Chapter 9, Problem 18CUR

To determine

To find: that length of $RX$ .

Answer to Problem 18CUR

  $RX=6$

Explanation of Solution

Given information:

In triangle $RST$

  $\begin{array}{l}RS=15\\ ST=27\\ TR=18\end{array}$

The bisector of $\angle T$ meets at X

Calculation:

Consider below diagram:

  

Use angle bisector theorem

  $\begin{array}{l}SX:RX=ST:RT\\ \frac{SX}{RX}=\frac{27}{18}=\frac{3}{2}\\ SX=\frac{3}{2}RX\\ SX+RX=15\\ \frac{3}{2}RX+RX=15\\ \frac{5}{2}RX=15\\ RX=6\end{array}$

Hence, $RX=6$ .