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    Question

    The perimeter of a rectangular field is 60 metres and

    its area is 137.5 m2 . What is the length of the diagonal of this field?
    A 20 metres Correct Answer Incorrect Answer
    B 22 metres Correct Answer Incorrect Answer
    C 25 metres Correct Answer Incorrect Answer
    D 21 metres Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the length and breadth of the rectangular field be ‘p’ metres and ‘q’ metres respectively Then, according to the question, 2 × (p + q) = 60 Or, (p + q) = 60/2 = 30…… (1) Also p × q = 137.5 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 302 – 2 × 137.5 Or, p2 + q2 = 625 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √625 = 25 metres

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