Answer:
AC = 70
BG = 38
GC = 28
AE = 63
Explanation:
The given parameters are;
The centroid of ΔABC = G
The length of FC = 35
The length of AG = 42
The length of BF = 57
The length of DG = 14
Given that the centroid is the intersection of the medians, we have;
FA = FC = 35 Definition of median line FB, (point F is the midpoint of AC)
AC = FA + FC = 35 + 35 = 70 by segment addition postulate
AC = 70
BG = 2/3 × BF = 2/3 × 57 = 38 Definition of median line BF
BG = 38
DG = 14 = 1/3 × DC Definition of median line
∴ DC = 3 × DG = 3 × 14 = 42
GC = 2/3 × DC = 2/3 × 42 = 28 Definition of median line DC
GC = 28
AG = 42 = 2/3 × AE Definition of median line AE
∴ AE = 3/2 × 42 = 63
AE = 63.