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    Question

    The perimeter of a rectangular field is 42 metres and

    its area is 108 m2 . What is the length of the diagonal of this field?
    A 10 metres Correct Answer Incorrect Answer
    B 8 metres Correct Answer Incorrect Answer
    C 15 metres Correct Answer Incorrect Answer
    D 7 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) = 42 Or, (p + q) = 42/2 = 21…… (1) Also p × q = 108 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 212 – 2 × 108 Or, p2 + q2 =441-216=225 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √225 = 15metres

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