In the triangle ABC, the medians BB₁ = 15 and CC₁ = 18, intersect at the point O, the angle BOS = 90 ° Find the area ABC?
March 5, 2021 | education
| Since BB1 and CC1 are the medians of the triangle ABC, point O divides them in a ratio of 2/1 starting from the vertices of the triangle.
Then ОВ = 10 cm, ОВ1 = 5 cm, ОВ = 12 cm, ОВ1 = 6 cm.
Triangles ОВ1С, ОВС, OC1В are rectangular, then, by the Pythagorean theorem:
BC ^ 2 = OC ^ 2 + OB ^ 2 = 144 + 100 = 244.
BC = 2 * √61 cm.
BC1 ^ 2 = OB ^ 2 + OC1 ^ 2 = 100 + 36 = 136.
BC1 = 2 * √34 cm.
Then AB = 2 * 2 * √34 = 4 * √34 cm.
CB1 ^ 2 = OC ^ 2 + OB1 ^ 2 = 144 + 25 = 169.
CB1 = 13 cm.
AC = 2 * CB1 = 2 * 13 = 26 cm.
Then Ravs = 26 + 4 * √34 + 2 * √61 = 68.94 cm.
Answer: The perimeter of the triangle is 68.94 cm.
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