Question

In Triangle FGH, GJ is an angle bisect or of G and perpendicular to FH. What is the length of FH in units?

Answer 1

Using the perpendicular bisector theorem, we have the following:

$GF=GH$

then we can write the following equation:

$3x-8=16$

solving for x, we have:

$\begin{gathered} 3x-8=16 \\ \Rightarrow3x=16+8=24 \\ \Rightarrow x=\frac{24}{3}=8 \\ \\ x=8 \end{gathered}$

we get x = 8. Then, the length of FH is:

$\begin{gathered} FH=FJ+JH=8+8=16 \\ \Rightarrow FH=16 \end{gathered}$

therefore, FH = 16