The median AM is drawn in triangle ABC, point K lies on side AB. The median KN = 0.5 of the triangle AKM

The median AM is drawn in triangle ABC, point K lies on side AB. The median KN = 0.5 of the triangle AKM is parallel to the line BC. Find the side length BC.

Consider the triangle ABM. Point H is the middle of the side AM, since, by condition, KH is the median of the triangle AKM. Also, according to the condition, the median KH is parallel to the side of the BC, and therefore to the BM, then the segment KN is the middle line of the triangle ABM.
Then ВM = 2 * KN = 2 * 0.5 = 1 cm.
AM is the median of the triangle ABC, then BM = MC = 1 cm, and then BC = 1 + 1 = 2 cm.
Answer: The length of the BC side is 2 cm.