Given the Centroid postulate:
The centroid is two-thirds of the distance from each vertex to the midpoint of the opposite side.
Each median is split into two parts such that the longer part is twice the length of the shorter part.
In this case, we have that:
AG= 10 ---> 2/3 (longer part) so, EG= (10/2/3) *1/3 = 5--> EG=5
CD=18 ----> 3/3 (total part) so, DG= 18*1/3= 6 (shorter part) and CG= 18*2/3=12 (longer part)
Now, we need to calculate BF, in this case, we know that sides AD and DB are congruent by Centroid postulate, so in order to calculate the unknown side BF, we can use the Pythagoras Theorem:
DB=8
DG = 6
BG is the Hypothenuse
--> BG^2 = DB^2 + DG^2 = 8^2 + 6^2
--> BG = sqrt[8^2+6^2]= 10
So, BG= 10
Now, in order to calculate the left side GF, we must consider that BG is the longer part and GF is the shorter part.
So BG=10----> 2/3 Total part = 10/(2/3) = 15 ---> GF = 15-10 = 5
ANSWERS:
BD = 8
AE=AG+EG=10+5= 15
AB=AD+DB=8+8 = 16
CG= 12
EG=5
DG=6