Using Thales' theorem, we have the following proportion:
[tex]\frac{GL}{GK}=\frac{GH}{GJ}[/tex]
So we have that:
[tex]\begin{gathered} \frac{12}{12+15}=\frac{4}{GJ} \\ \frac{12}{27}=\frac{4}{GJ} \\ \frac{3}{27}=\frac{1}{GJ} \\ \frac{1}{9}=\frac{1}{GJ} \\ GJ=9 \end{gathered}[/tex]
So the length of GJ is 9.
