Answer:
FG = 18
Explanation:
There is a simpler solution:
It has to do with the interior angle bisector theorem. (the illustration with the angle marks and the line show that it is being bisected)
Which will divide the opposite side into segments whose lengths have the same ratio as the adjacent sides of the bisected angle.
x / 24 = x + 10 / 54 →
54x = 24(x + 10) →
54x = 24x + 240 →
30x = 240 →
x = 8.
Since the expression x + 10 represents the length of FG, it's length must be 18.