Chapter 13, Problem 9STP

To determine

Find the value of $\left(x\right)$ for the triangle shown below if $AD$ bisects $\angle CAB$ .

  

Answer to Problem 9STP

The value of $\left(x\right)$ is $3$ .

Explanation of Solution

Given information: The given triangle is shown as in which $AD$ bisects $\angle CAB$ .

  

Calculation: By angle bisector theorem in triangle ABC,

  $\begin{array}{c}\frac{AB}{AC}=\frac{BD}{DC}\\ \frac{7x-5}{10}=\frac{2x+2}{5}\\ 35x-25=20x+20\mathrm{....}\left(\text{Cross multiply}\right)\\ 15x=45\\ x=3\end{array}$

Hence the value of $\left(x\right)$ is $3$ .