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NDA 2017 Maths · Mathematics · Application of Derivatives · easy

A wire of length 20 cm is bent into a rectangle. The maximum possible area of the rectangle is

Single correct option

A wire of length 2020 cm is bent into a rectangle. The maximum possible area of the rectangle is
  1. A. 2020 cm2^2
  2. B. 5050 cm2^2
  3. C. 2525 cm2^2
  4. D. 100100 cm2^2
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Answer: (C) 2525 cm2^2

If the sides are xx and 10−x10-x, the area is x(10−x)x(10-x), which is maximum at x=5x=5, i.e. a square, giving 2525. Taking the full length as the semi-perimeter gives 100100, and 5050 is the area of a 5×105\times10 rectangle which cannot occur.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake