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Question 310010
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Application of Derivatives: JEE Main MCQ

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JEE MainHardQuestion 310010

Question

The maximum area of a rectangle with perimeter 20 m is:
  1. A
    25 m²
    Correct
  2. B
    20 m²
  3. C
    100 m²
  4. D
    10 m²

Correct answer

25 m²

Explanation

Let sides be x and y: 2(x+y) = 20 → x+y = 10. Area A = xy. By AM-GM: xy ≤ ((x+y)/2)² = 25. Maximum area = 25 m² when x = y = 5 (square).

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