Chapter 8.5, Problem 12PSA

To determine

To find the length of side.

Answer to Problem 12PSA

The length of side is 5.6

Explanation of Solution

Given information:

  $\overleftrightarrow{GJ}$ bisects $\angle FGH$

  $\begin{array}{l}FG=10,\\ GH=8,\\ FJ=7\end{array}$

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:

  

It is given that,

  $\overleftrightarrow{GJ}$ bisects $\angle FGH$

  $\begin{array}{l}FG=10,\\ GH=8,\\ FJ=7\end{array}$

Using Angle Bisector Theorem, we get

  $\begin{array}{l}\frac{FG}{FJ}=\frac{GH}{JH}\\ \frac{10}{7}=\frac{8}{JH}\\ 10(JH)=56\\ \therefore JH=\frac{56}{10}=5.6\end{array}$