Answer:
GB = 7
BE = 10.5
AG = 10
DG = 5
FG = 3·x
CF = 9·x
Explanation:
The given parameters are;
The centroid of the ΔABC = G
Segments CF, BE, and AD are median lines
EG = 3.5 Given
∴ EG = 1/3 × BE by definition of the properties of median line
∴ BE = 3 × EG = 3 × 3.5 = 10.5
BE = 10.5
GB = 2/3 × BE = 2/3 × 10.5 = 7 by definition of the properties of median line BE
GB = 7
Similarly;
Given that AD = 15, AG = 2/3 × AD = 2/3 × 15 = 10 by definition of the properties of median line AD
AD = 10
DG = 1/3 × AD = 1/3 × 15 = 5 by definition of the properties of median line AD
DG = 5
Similarly;
Given CG = 6·x
FG = 1/3 × CF
CF = 3 × FG
CG = 2/3 × CF = 2/3 × 3 × FG
∴ CG = 2 × FG
FG = CG/2 = 6·x/
2 = 3·x
FG = 3·x
CF = 3 × FG = CF = 3 × 3 × x = 9·x
CF = 9·x