CDS 2026 (I) Elementary Mathematics, question 62

Topic: Mensuration

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Q62

A square and a rectangle have the same perimeter pp and their areas differ by qq units. What is the square of the difference between the length and breadth of the rectangle ?

  1. (a) 1.5q1.5q
  2. (b) 2q2q
  3. (c) 2.5q2.5q
  4. (d) 4q4qCorrect answer

Solution.

Answer: (d) 4q4q

  1. Let the rectangle sides be l and b.
  2. Equal perimeters make the square's side (l+b)/2(l + b)/2.
  3. The square has the greater area, so q=(l+b)2/4−lb=(l−b)2/4q = (l + b)^{2}/4 - lb = (l - b)^{2}/4.