Question

In (triangle ABC), (G) is the centroid and (BE = 21). Find (BG) and (GE).

a) (BG = 8, GE = 13)
b) (BG = 9, GE = 12)
c) (BG = 6, GE = 15)
d) (BG = 7, GE = 14)

Answer 1

In triangle ABC, the centroid G divides each median in a ratio of 2:1. To find BG and GE, calculate two-thirds and one-third of the length of BE, respectively.

Step-by-step explanation:

In triangle ABC, the centroid G divides each median in a ratio of 2:1. This means that BG is two-thirds of the length of the median BE, and GE is one-third of the length of BE.

Given that BE = 21, we can calculate:

BG = (2/3) * 21 = 14.

GE = (1/3) * 21 = 7.

Therefore, the correct answer is (BG = 14, GE = 7).