If a farmer uses 40 metres of fencing to enclose a rectangular field, what is the maximum area he can enclose?
Answer
100
The correct answer is 100 — Hence the farmer can enclose at most 100 square metres with 40 m of fence.
Step-by-step solution
- For a fixed perimeter, a square encloses the maximum area among rectangles.
- Given the perimeter P = 40 m, the side of the square is P ÷ 4 = 10 m.
- The maximum area is side² = 10² = 100 m².
- Hence the farmer can enclose at most 100 square metres with 40 m of fence.
Common mistake: choosing a rectangle with unequal sides instead of a square
Concept tested: maximum area for given perimeter
Published · How this solution was prepared and checked
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