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      Question

      In triangle ABC, DE is drawn parallel to BC, meeting AB

      at D and AC at E. If AD : DB = 3 : 2 and the area of triangle ADE is 45 cm², find: (a) the area of triangle ABC, (b) the ratio of perimeters of ΔADE and ΔABC.
      A 225 cm² and 1:5 Correct Answer Incorrect Answer
      B 125 cm² and 3:5 Correct Answer Incorrect Answer
      C 105 cm² and 3:4 Correct Answer Incorrect Answer
      D 125 cm² and 7:5 Correct Answer Incorrect Answer

      Solution

      ATQ, AD : DB = 3 : 2 ⇒ AB = 3k + 2k = 5k AD = 3k Since DE ∥ BC, triangles ADE and ABC are similar. Linear scale factor (ABC : ADE) = AB/AD = 5k / 3k = 5/3 (a) Area scale factor = (5/3)² = 25/9 Area(ABC) = (25/9) × 45 = 25 × 5 = 125 cm² (b) Perimeter ratio of similar triangles = ratio of corresponding sides = 3 : 5 (ADE : ABC). Answer: (a) Area of ΔABC = 125 cm² (b) Perimeter(ΔADE) : Perimeter(ΔABC) = 3 : 5.

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