see the attached figure to better understand the problem
we know that
The point G is where all medians intersect and is often described as the triangle's center of gravity or centroid. It is formed by the intersection of the medians. The centroid divides each median in a ratio of [tex] \frac{2}{1} [/tex]
so
[tex] \frac{AG}{GF} =\frac{2}{1} \\\\ \frac{5x+4}{3x-1}=\frac{2}{1}\\ \\ (3x-1)*2=5x+4\\ \\ 6x-2=5x+4 \\\\ 6x-5x= 4+2\\\\ x=6\ units [/tex]
Find the value of FA
[tex] FA=(5x+4)+(3x-1)\\
FA=8x+3\\
FA=8*6+3\\
FA=51 units [/tex]
therefore
the answer is
[tex] 51 units [/tex]
