Chapter 12, Problem 14CUR

To determine

To find: The value of $x$ in the given triangle.

Answer to Problem 14CUR

The value of $x$ in the given triangle is $8$ .

Explanation of Solution

Given information: A triangle with sides $12$ , $9$ and $14$ .

  

Calculation:

In the diagram a triangle is given with two sides as $12$ and $9$ , base $14$ and an angle bisector dividing the base.

  

Since an angle bisector divides the base into the ratio of its adjacent sides.

By angle bisector formula,

  $\begin{array}{c}\frac{x}{14-x}=\frac{12}{9}\\ \frac{x}{14-x}=\frac{4}{3}\\ 3x=4\left(14-x\right)\\ 3x=56-4x\end{array}$

Solve further.

  $\begin{array}{c}3x+4x=56\\ 7x=56\\ x=\frac{56}{7}\\ x=8\end{array}$

Therefore, the value of $x$ in the given triangle is $8$ .