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      Question

      In triangle ABC, DE is drawn parallel to BC,

      intersecting AB at D and AC at E. If AD : DB = 2 : 1 and area of triangle ADE is 24 cm², find: (i) area of triangle ABC, (ii) area of trapezium BDEC.
      A 54 cm² and 30 cm² Correct Answer Incorrect Answer
      B 40 cm² and 25 cm² Correct Answer Incorrect Answer
      C 10 cm² and 20 cm² Correct Answer Incorrect Answer
      D 50 cm² and 60 cm² Correct Answer Incorrect Answer

      Solution

      AD : DB = 2 : 1 ⇒ AB = AD + DB = 3 parts So AB : AD = 3 : 2 Since DE ∥ BC, triangles ADE and ABC are similar. Linear scale factor (ABC : ADE) = AB/AD = 3/2 Area scale factor = (3/2)² = 9/4 (i) Area(ABC) = (9/4) × Area(ADE) = (9/4) × 24 = 54 cm² (ii) Area of trapezium BDEC = Area(ABC) − Area(ADE) = 54 − 24 = 30 cm²

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