Final answer:
The lengths KM, JO, and KP were found using the property of centroids dividing medians in a 2:1 ratio. KM was calculated to be 16 units, KP to be 12 units, and JO to be 12 units.
Step-by-step explanation:
Lengths relevant to a geometric shape, likely a triangle or a quadrilateral given the mention of medians meeting at a centroid (point Q). In triangles, a key property of the median is that it is divided into segments that are in the ratio 2:1 by the centroid. Specifically, the centroid divides the median into two segments, where the segment connecting the centroid to the midpoint of the opposite side is twice as long as the segment from the centroid to the vertex. Applying this property, if KQ is 4 (being the shorter segment from the centroid to the vertex K of the median KP), then the longer segment (from the centroid to the midpoint of JL) would be twice that length, which is 8 units. This makes the full length of median KP to be 4 + 8 = 12 units. For median LM, if LM = 36 units and the centroid divides this median in the 2:1 ratio as well, then MQ (the segment from M to the centroid Q) would be one-third of 36 units, which is 12 units, since QM would be the longer segment. Consequently, KM would be the sum of KQ and QM, equating to 4 + 12 = 16 units. Lastly, for median JN, if QN = 8 units (the shorter segment), then JQ (as the longer segment) will be twice that, which is 16 units. Hence, the entire median JN would be 8 + 16 = 24 units, and since JO is half of this median (because O would be the midpoint of JL), JO would measure 12 units.