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      Question

      If the lengths of three medians of a triangle are 18 cm,

      24 cm and 30 cm, then what will be the area (in sq. cm) of the triangle?
      A 280 cm² Correct Answer Incorrect Answer
      B 288 cm² Correct Answer Incorrect Answer
      C 250 cm² Correct Answer Incorrect Answer
      D 320 cm² Correct Answer Incorrect Answer

      Solution

      D = 18 cm. BE = 24 cm CF = 30 cm Let G be the centroid of a triangle. Length of AG = 2/3 × 18 = 12 cm Length of BG = 2/3 × 24 = 16 cm Length of CG = 2/3 × 30 = 20 cm (Centroid divides median in the ratio of 1 : 2) Area of ∆AGB = 1/2 × AG × BG = 1/2 × 12 × 16 = 96 cm² Area of ∆ABC = 3 × Area of ∆AGB = 3 × 96 = 288 cm²

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