Question

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

Answer 1

Answer: Choice C) BG = 6, GE = 12

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Step-by-step 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

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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