I'm offering 10 points, only answer if you're smart

Challenge accepted!!
This is more simple than you think, it's actually quite similar to that of diameter and radius, except this is triangles instead of circles. 

The "centroid" of a triangle is known as the center of mass, everything around it is perfectly evenly balanced from that point, and for triangles, it's the point of intersection for all medians. Now, when dealing with the centroid of triangles, there is a rule that always applies to every median: the distance from a vertex of the triangle to the centroid is ALWAYS twice that of the distance to the midpoint, which would be on the side opposite of the chosen vertex. 

Let's call the identified side "B", the Centroid "A" and the Vertex "C"

Point B to point A is half the distance of point A to point C, as point B occurs on the opposite side of point C. 

This is the same for EVERY median. You could choose any line, and any vertex, and the answer would be the same. The side, if it's opposite of the vertex, is always half the distance to the centroid as the Vertex to the centroid is. 

Your answer A "Twice"

~Hope you better understand, and that this helped!

Add up all the sides