Answer: The required length of FG is 15 units.
Step-by-step explanation: Given that the length of the segment EG is 25 units and the point F is \(\dfrac{2}{5}\) of the way between E and G.
We are to find the length of FG.
The given information is shown in the attached figure below.
Since the point F is \(\dfrac{2}{5}\) of the way between E and G, so we must have
\(EF=\dfrac{2}{5}\times EG\\\\\\\Rightarrow EF=\dfrac{2}{5}\times25\\\\\Rightarrow EF=10.\)
Therefore, the length of FG is given by
\(FG=EG-EF=25-10=15.\)
Thus, the required length of FG is 15 units.
