Question

Given that L is the centroid of triangle FGH, find LG.

Answer 1

Well the centroid is the point that connects the median of a side with the opposite vertex. This means that each line is split i half. Notice that line HG is split in half by point K. that means that each of the segments that K splits is equal. so we know
HK = KG

and we know
HK = 3x
KG = x + 8

since
HK = KG then
3x = x + 8
2x = 8
x = 4

now we have x. we know that the each line that runs from a midpoint to a vertex is seperated by the centroid. the 2 line segments are a 2:1 ratio. so
2*JL = 1LG

we know
JL = x + 3

so
2 * (4 + 3) = LG
LG = 14