Given the triangle below with centroid G, determine the following values. If EG=3.5, then GB= and BE= If AD=15, then AG= and DG= If CG=6x, then FG- and CF=

GB = 7

BE = 10.5

AG = 10

DG = 5

FG = 3·x

CF = 9·x

Step-by-step 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