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      Question

      A rectangular wheat field has an area of 1682 sq.metres

      whereas its perimeter is 29 x 3 x 2 metres. If the length and breadth are positive integers, then find the perimeter. (It is known that a, b, c are positive integers.)
      A 174 metres Correct Answer Incorrect Answer
      B 58 metres Correct Answer Incorrect Answer
      C 116 metres Correct Answer Incorrect Answer
      D 87 metres Correct Answer Incorrect Answer

      Solution

      The expression for the perimeter shows that the perimeter has the factors 29, 3, and 2 to some powers a, b, and c respectively. So, let us factoise the options: 174 = 2 ├Ч 3 ├Ч 29 58 = 2 ├Ч 29┬а 116 = 2 ├Ч 2 ├Ч 29 87 = 3 ├Ч 29 From the above, we can see that only option 1 has all three as its factors. тИ┤ The perimeter of the field is 174 m.

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