Question

    Find the area of a rhombus. A. Sum of the squares

    of the diagonals is 256 m². B. Perimeter of the rhombus is 32 m. C. Ratio of one diagonal and the side is 3:8 Directions – : The following questions are accompanied by three statement A, B and C. you have to determine which statement (s) is /are necessary/ sufficient to answer the question.
    A Only A and B together Correct Answer Incorrect Answer
    B Only C Correct Answer Incorrect Answer
    C C and either A or B Correct Answer Incorrect Answer
    D Any two of them Correct Answer Incorrect Answer
    E All statements are required Correct Answer Incorrect Answer

    Solution

    If d₁ and d₂ be the diagonals and a the length of the side of the rhombus then From 1: d₁²+ d₂² = 4a² = 256 a² = 64 a = 8
    From 2:

    Perimeter = 4a
    32 = 4a a = 8
    From 3: d₁ : a = 3 : 8
    Therefore, by combining C and either A or B, a = 8, d₁ = 3 so we can find d₂ by using, d₁²+ d₂² = 4a² then we can find area of rhombus = 1/2 * d1 * d2 Hence by combining C and either A or B are required to answer as A & B are same.

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