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      Question

      The perimeter of a rectangular field is 44 metres and its area is 114 m2 . What is the length of the diagonal of this field?

      A 12 metres Correct Answer Incorrect Answer
      B 13 metres Correct Answer Incorrect Answer
      C 16 metres Correct Answer Incorrect Answer
      D 17 metres Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the length and breadth of the rectangular field be β€˜p’ metres and β€˜q’ metres respectively Then, according to the question, 2 Γ— (p + q) = 44 Or, (p + q) = 44/2 = 22…… (1) Also p Γ— q = 114 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 222 – 2 Γ— 114 Or, p2 + q2 = 256 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √256 = 16 metres

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