Question

1. in △ace, g is the centroid and be = 12. find bg and ge. bg = 4, ge = 8 bg = 8, ge = 4 bg = 3, ge = 9 bg = 6, ge = 6

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1. That is, if a median is divided by the centroid, the segment from the vertex to the centroid is twice as long as the segment from the centroid to the mid - point of the opposite side. Let $BG = 2x$ and $GE=x$.

Step2: Set up an equation using the length of the median

Since $BE=BG + GE$ and $BE = 12$, we have $2x+x=12$.
Combining like terms gives $3x = 12$.
Dividing both sides by 3, we get $x = 4$.

Step3: Find the lengths of $BG$ and $GE$

Since $BG = 2x$ and $x = 4$, then $BG=8$.
Since $GE=x$, then $GE = 4$.

Answer:

BG = 8, GE = 4