In triangle ACE. G is the centroid and BE = 15 BE is a median. Find BG and GE

Answer 1

In a triangle, the centroid is a point of concurrence of the medians. The centroid divides each median into segments in the ratio of 2:1, where the longer segment is closer to the vertex.

Let's assume BG = 2x and GE = x.
Therefore, BE = BG + GE = 2x + x = 3x = 15.

Solving this equation, we get:
3x = 15
x = 15/3
x = 5

So, BG = 2x = 2 * 5 = 10
And GE = x = 5.

Therefore, BG = 10 and GE = 5.