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    Question

    The area of a rhombus is given as 384 cm², and its

    perimeter measures 80 cm. Determine the total length of its two diagonals.
    A 42 cm Correct Answer Incorrect Answer
    B 21 cm Correct Answer Incorrect Answer
    C 28 cm Correct Answer Incorrect Answer
    D 56 cm Correct Answer Incorrect Answer

    Solution

    Length of each side of the rhombus = 80 ÷ 4 = 20 cm

    Let the length of longer diagonal be '2x' cm and that of smaller diagonal be '2y' cm.

    So, (1/2) X 2x X 2y = 384

    Or, xy = 192Image

    Now, since the diagonals of a rhombus are perpendicular bisectors of each other. So, ABC is a right angled triangle.

    And, in triangle ABC, we have

    x2 + y2 = 400

    Since, (x + y)2 = x2 + y2 + 2xy

    So, (x + y)2 = 400 + 2 X 192

    Or, (x + y)2 = 784

    So, x + y = 28

    So, required sum = 28 X 2 = 56 cm

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