4
advanced-math

A rectangle has a perimeter of 36 cm. What dimensions maximize the area?

A

9 cm by 9 cm

B

10 cm by 8 cm

C

12 cm by 6 cm

D

18 cm by 18 cm

Correct Answer: A

Choice A is the correct answer. For a fixed perimeter, a rectangle's area is maximized when it is a square.

  1. Perimeter P=4s=36P = 4s = 36.
  2. Side s=9s = 9.
  3. Dimensions: 9 cm by 9 cm. Area = 81.

Choice B is incorrect because area is 80. Choice C is incorrect because area is 72. Choice D is incorrect because perimeter would be 72.