imo class 12 application of derivatives

Of all the rectangles of a given perimeter, the one with the greatest area is a:

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Of all the rectangles of a given perimeter, the one with the greatest area is a:

  • A. Square
  • B. Rectangle with length twice breadth
  • C. Rectangle with length thrice breadth
  • D. Rhombus

Answer: A) Square

Explanation: Let perimeter be P = 2(l+b). Area A = l(P/2 - l). A' = P/2 - 2l = 0 implies l = P/4, which means b = P/4. The rectangle is a square.

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