# In an equal coastal triangle ABC with base AC, the medians intersect at point O. Find the area

In an equal coastal triangle ABC with base AC, the medians intersect at point O. Find the area of triangle ABC if OA = 13 cm. OB = 10 cm.

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

Then OB / OM = 2/1.

ОМ = ОВ / 2 = 10/2 = 5 cm.

Then BM = BО + ОМ = 10 + 5 = 15 cm.

In an isosceles triangle, the median drawn to the base also has its height and bisector, then BM is perpendicular to AC, and triangle AOM is rectangular.

By the Pythagorean theorem, in the right-angled triangle AOM, we determine the length of the leg AM.

AM ^ 2 = AO ^ 2 – OM ^ 2 = 169 – 25 = 144.

AM = 12 cm.Then AC = 2 * AM = 2 * 12 = 24 cm.

Determine the area of ​​the triangle ABC.

Savs = AC * BM / 2 = 15 * 24/2 = 180 cm2.

Answer: The area of ​​the triangle is 180 cm2. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.