Chapter 8.5, Problem 26PSC

To determine

To find the perimeter of the triangle.

Answer to Problem 26PSC

The perimeter of the triangle is 42.25

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

  $\begin{array}{l}\frac{FG}{GH}=\frac{FK}{KJ}\\ \frac{x-2}{9}=\frac{4}{x+3}\\ (x-2)(x+3)=36\\ x^2+x-42=0\\ (x-6)(x+7)=0\\ x=6\\ \frac{FG}{FH}=\frac{5}{y}\\ \frac{4}{13}=\frac{5}{y}\\ y=\frac{65}{4}=16.25\end{array}$

Perimeter of ΔHJF

  $\begin{array}{l}=4+9+16.25+9+4\\ =42.25\end{array}$