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A farmer wants to enclose a rectangular field having an area of 180 square metres. He wants to use the least amount of fencing possible. What should be the length and breadth of the field?

hard MCQ 3 marks Class 4 · Mathematics · Fields and Fences
  1. A. Length 18 m, Breadth 10 m
  2. B. Length 12 m, Breadth 15 m
  3. C. Length 6√5 m, Breadth 6√5 m
  4. D. Length 9 m, Breadth 20 m
Answer
C. Length 6√5 m, Breadth 6√5 m

The correct answer is C. Length 6√5 m, Breadth 6√5 m — Therefore the optimal dimensions are length = 6√5 m and breadth = 6√5 m.

Step-by-step solution

  1. For a fixed area, the rectangle with the least perimeter is a square.
  2. Let the side of the square be s metres; then s² = 180.
  3. Solve for s: s = √180 = √(36×5) = 6√5 metres.
  4. Thus both length and breadth should be 6√5 m to minimise fencing.
  5. Therefore the optimal dimensions are length = 6√5 m and breadth = 6√5 m.
Common mistake: thinking any rectangle would use the least fencing

Concept tested: optimal fencing for given area

Published · How this solution was prepared and checked

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