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      Question

      In ∆ ABC, MN ‖ BC, the area of quadrilateral

      MBCN=130 sqcm. If AN : NC = 4 : 5, then the area of ∆ MAN is:
      A 40 cm^2 Correct Answer Incorrect Answer
      B 45 cm^2 Correct Answer Incorrect Answer
      C 32 cm^2 Correct Answer Incorrect Answer
      D 65 cm^2 Correct Answer Incorrect Answer

      Solution

      AN : NC = 4 : 5 AC = AN + NC = 4 + 5 = 9 MN ‖ BC So, ∆ ABC ~ ∆ MAN Areaof △ MAN 42 Areaof△ ABC = 92 Areaof△ MAN 16 Areaof△ ABC = 81 Let the area of be 16x and be 81x. Area of quadrilateral MBCN =130 sqcm Area of - area of =130 sqcm 81x - 16x = 130 x = 130/65 = 2 Area of ∆ MAN = 16x = 16 2 = 32 sqcm.

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