Question
In a triangle ABC, the lengths of the medians from A, B, and C are 5 cm, 6 cm, and 7 cm, respectively. What is the area of the triangle?
Solution
The area of a triangle can be calculated using the formula involving medians: Area = (4/3) × √[s(s - m₁)(s - m₂)(s - m₃)], where m₁, m₂, m₃ are the medians, and s = (m₁ + m₂ + m₃) / 2 = (5 + 6 + 7) / 2 = 9 cm. Substituting into the formula, Area = (4/3) × √[9(9 - 5)(9 - 6)(9 - 7)] = (4/3) × √[9 × 4 × 3 × 2] = (4/3) × √216 = (4/3) × 14.7 = 19.6 cm² Correct answer: b) 19.6 cm²
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