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NDA 2 2025 Maths, question 96

Topic: Differential calculus

Q96

A wire of length 20 cm20\text{ cm} is to be bent into a rectangle. Which of the following statements is/are correct?

I. The rectangle of the largest area is the square.

II. It is possible to form a rectangle of an area of 27 cm227\text{ cm}^{2}.

Select the answer using the code given below.

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. If the sides are x and 10−x, the area is x(10−x)=25−(x−5)²≤25 cm².
  2. The maximum occurs for equal sides, a square.
  3. An area of 27 cm² is impossible, so only I is true.