In the MNK triangle, the medians MP and NE intersect at point O and are equal to 12 cm and 15 cm

In the MNK triangle, the medians MP and NE intersect at point O and are equal to 12 cm and 15 cm, respectively. Find the area of the triangle MOE if MP is perpendicular to NE.

The medians of the triangle, at the point of their intersection, are divided by a ratio of 2/1, starting from the apex of the triangle.

Then OE = HE / 3 = 15/3 = 5 cm, MO = 2 * MR / 3 = 2 * 12/3 = 8 cm.

By condition, МР is perpendicular to HE, then the triangle MOE is rectangular.

Smoe = MO * OE / 2 = 8 * 5/2 = 20 cm2.

Answer: The area of the MOE triangle is 20 cm2.