In rectangular ABC (C = 90 °) BC = 9. The medians of the triangle meet at point O, OB = 10. Find the area of triangle ABC.
The medians of the triangle, at the point of their intersection, are divided in the ratio of 2/1, starting from the top, then OB = 2 * OM.
ОМ = ОВ / 2 = 10/2 = 5 cm, then ВМ = ОВ + ОМ = 10 + 5 = 15 cm.
From the right-angled triangle of the BCM, according to the Pythagorean theorem, we determine the length of the CM leg.
CM ^ 2 = BM ^ 2 – BC ^ 2 = 225 – 81 = 144.
CM = 12 cm.
Since BM is the median, then AM = CM = 12 cm, then AC = 2 * CM = 2 * 12 = 24 cm.
Determine the area of the triangle ABC.
Savs = AC * BC / 2 = 24 * 9/2 = 108 cm2.
Answer: The area of the triangle is 108 cm2.
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