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MHT CET202611 April 2026Morning ShiftMathematicsApplication of DerivativesActual

A wire of length 64 m is to be bent to form a rectangle such that its area is maximum, then its area is.....

Options

  1. A156 sq.m
  2. B324 sq.m
  3. C256 sq.m
  4. D320 sq.m

Correct answer

C. 256 sq.m

Step-by-step solution

Let the length and breadth of the rectangle be x and y respectively. The perimeter of the rectangle is equal to the length of the wire. 2(x + y) = 64 x + y = 32 The area of the rectangle is A = xy . Using the AM-GM inequality for positive numbers x and y : x + y 2 xy 32 2 A 16 A A 256 The maximum area of the rectangle is 256 sq.m, which occurs when x = y = 16 m (when the rectangle is a square).

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