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    Question

    The perimeter of a rectangular field is 70 metres and its area is 100.5 m2 . What is the length of the diagonal of this field?

    A 33 metres Correct Answer Incorrect Answer
    B 22 metres Correct Answer Incorrect Answer
    C 32 metres Correct Answer Incorrect Answer
    D 30 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) = 70 Or, (p + q) = 70/2 = 35…… (1) Also p × q = 100.5 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 352 – 2 × 100.5 Or, p2 + q2 = 1024 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √1024 = 32 metres

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