What is the length of one side of a square that has the same area as a circle with radius

Question

What is the length of one side of a square that has the same area as a circle with radius 2 ?

Accepted Answer

Choice C is correct. The area A of a circle with radius r is given by the formula . Thus, a circle with radius 2 has area , which can be rewritten as . The area of a square with side length s is given by the formula . Thus, if a square has the same area as a circle with radius 2, then . Since the side length of a square must be a positive number, taking the square root of both sides of gives . Using the properties of square roots, can be rewritten as , which is equivalent to . Therefore, . Choice A is incorrect. The side length of the square isn&rsquo;t equal to the radius of the circle. Choices B and D are incorrect and may result from incorrectly simplifying the expression .

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