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 × 3 × 29 58 = 2 × 29  116 = 2 × 2 × 29 87 = 3 × 29 From the above, we can see that only option 1 has all three as its factors. ∴ The perimeter of the field is 174 m.

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