In triangle ACE, G is the centroid and BE = 18. Find BG and GE. a BG=12, GE=6
b BG=4 1/2, GE=13 1/2
c BG=6, GE=12
d BG=9 GE=9

Choice C)  BG = 6, GE = 12

Explanation:

The centroid G cuts the median segment BE such that BG is 1/3 of BE, and GE is 2/3 of BE.

So,

BG = (1/3)*BE = (1/3)*18 = 6

GE = (2/3)*BE = (2/3)*18 = 12

Put another way: GE is twice as long as BG

Let x = BG. This means 2x = GE

Leading to

BG+GE = BE

x+2x = 18

3x = 18

x = 18/3

x = 6 = BG

2x = 2*6 = 12 = GE

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it

a. is correct