Answer:
[tex]\overline{FM}=20[/tex]
[tex]\overline{MG}=20[/tex]
Therefore,
[tex]\overline{FG}=40[/tex]
Step-by-step explanation:
Once M is the midpoint of FG, we conclude that
FM is half of FG and MG is half of FC and hence, FM = MG.
Given:
[tex]\overline{FM}=12x-4[/tex]
[tex]\overline{MG}=5x+10[/tex]
[tex]\overline{FM} = \overline{MG} \implies 12x-4 = 5x+10 \implies 7x=14 \implies \boxed{x = 2}[/tex]
So,
[tex]\overline{FM}=12x-4 = 12(2)-4=24-4=20[/tex]
[tex]\overline{MG}=5x+10 = 5(2)+10 = 10+10 =20[/tex]
