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    Question

    The perimeter of a rectangular field is 22 metres and

    its area is 20 m^2 . What is the length of the diagonal of this field?
    A 9 metres Correct Answer Incorrect Answer
    B 11 metres Correct Answer Incorrect Answer
    C 12 metres Correct Answer Incorrect Answer
    D 13 metres 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) = 22 Or, (p + q) = 22/2 = 11…… (1) Also p × q = 20 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 112 – 2 × 20 Or, p2 + q2 = 81 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √81 = 9 metres

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