Answer:
10 units
Step-by-step explanation:
It's important to know that the centroid is always two-thirds of the median. Which means
[tex]AG=\frac{2}{3}FA\\ x+9=\frac{2}{3}(5x+x+9)\\ x+9=\frac{2}{3}(6x+9) \\x+9=4x+6\\9-6=4x-x\\3x=3\\x=1[/tex]
Which means [tex]AG=x+9=1+9=10[/tex].
But, the centroid has always the same distance from each vertex, which means
[tex]AG=BG=10[/tex]
Therefore, BG is 10 units long.
