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JAMB Mathematics 2001 Question 37

Question 37

Differentiation

Find the dimensions of the rectangle of greatest area which has a fixed perimeter p.

  1. A.Square of sides p/4
  2. B.Square of sides p/2
  3. C.Square of sides p
  4. D.Square of sides 2p
Show the answer and explanation

Answer: A (Square of sides p/4)

Explanation

With sides x and p/2 − x, the area x(p/2 − x) is greatest when x = p/4. Both sides are then p/4, a square.