In an isosceles triangle ABC with base AC, the medinans intersect at point O.

| March 23, 2021 | education

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

By the property of the medians of the triangle, they are divided at the point of their intersection in the ratio of 2/1 starting from the vertex. Then ВO = 2 * OB1.

OB1 = ВO / 2 = 10/2 = 5 cm.

Then BB1 = ВO + OB1 = 10 + 5 = 15 cm.

The median BB1, drawn to the base of the AC, is the height of the triangle, then the triangle AOB1 is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg AB1.

AB1 ^ 2 = AO1 ^ 2 – OB1 ^ 2 = 169 – 25 = 144.

AB1 = 12 cm, then AC = 2 * AB1 = 2 * 12 = 24 cm.

Determine the area of the triangle ABC.

Savs = AC * BB1 / 2 = 24 * 15/2 = 180 cm2.

Answer: The area of the triangle is 180 cm2.



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