Chapter 8.5, Problem 20PSB

To determine

To find the perimeter of the triangle.

Answer to Problem 20PSB

The perimeter of the triangle is 40.

Explanation of Solution

Given information:

  $\overleftrightarrow{GK}$ is parallel to $\overleftrightarrow{HJ}$

Formula used:

The below theorem is used:

Angle bisector theorem states that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

Calculation:

  

Using Angle Bisector Theorem, we get

  $\begin{array}{l}\frac{9}{x+3}=\frac{4}{x-2}\\ 9x-18=4x+12\\ 5x=30\\ x=6\\ \frac{18}{9}=\frac{y}{7}\\ 126=9y\\ y=\frac{126}{9}=14\end{array}$

Perimeter of ΔHFJ

  $\begin{array}{l}=(x+3+9)+(4+x-2)+y\\ =2x+y+14\\ =2(6)+14+14\\ =40\end{array}$