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      Question

      The lengths of three medians in a triangles are 6 cm, 8

      cm, 10 cm. What is the area of that traingle (in cm 2 )?
      A 8 cm² Correct Answer Incorrect Answer
      B 32 cm² Correct Answer Incorrect Answer
      C 72 cm² Correct Answer Incorrect Answer
      D 128 cm² Correct Answer Incorrect Answer

      Solution

      Here s = (a+ b+ c )/2 = (6 + 8 +10) /2 = 24/2 = 12 cm If a, b & c are medians of any triangle , then area of the triangle = 4/3 √(s(s - a)(s - b)(s - c)) = 4/3 √(12(12 - 6)(12 - 8)(12 - 10)) = 4/3 √(12 × 6 × 4 × 2) = (4/3) × 24 = 32 cm²

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