The concurrency of medians theorems indicates that the lengths of the segments are;
QM = 12
JQ = 16
KP = 6
The steps used to find the distances from the vertices to the centroid and the midpoint on the facing side are presented as follows;
The concurrency of medians theorem indicates that we get;
QL = (2/3) × LM, therefore, QM = (1/3) × LM
LM = 36
QM = (1/3) × 36
(1/3) × 36 = 12
QM = 12
JQ = (2/3) × JN
QN = (1/3) × JN, therefore, JN = QN/(1/3)
JN = 8/(1/3)
8/(1/3) = 24
JN = 24
JQ = (2/3) × 24
JQ = 16
KQ = (2/3) × KP
KP = KQ/(2/3)
KP = 4/(2/3)
KP = 6