Question

The medians of ADEF are DK, EL, and FJ. They meet at a single point M.

(In other words, M is the centroid of ADEF.)
Suppose ML = 9, MJ=8, and DK = 24.
Find the following lengths.
Note that the figure is not drawn to scale.

Answer 1

FJ = 24

DM = 16

EM = 18

Explanation:

I remember that the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side. Therefore the median is split into two parts where one side is always twice as long as the other. So given that segment ML is 8, the other part of the segment (DM) must be 16 as 16 is 2/3 of 24 and 8 is 1/3 of 24 and 1/3 + 2/3 = 1.

Therefore, since MJ is 8, FM must be twice as long so it is 16. Add them up to get FJ, and 8 + 16 is 24.

Finally for EM, since the longer part of the median is twice the length of the smaller part EM must be 18 since 9 × 2 = 18, and 2/3 of 18 is 27, 9 + 18 = 27.