Set 9: Quadratic Equations (Intermediate)

Explanation

Answer: A

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

9 cm by 9 cm

✓ Correct

10 cm by 8 cm

12 cm by 6 cm

18 cm by 18 cm

Detailed Explanation

Choice A is correct. Choice A is the correct answer. For a fixed perimeter, a rectangle's area is maximized when it is a square. 1. Perimeter $P = 4 s = 36$ . 2. Side $s = 9$ . 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.

Key Steps:

•

The correct answer is 9 cm by 9 cm

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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