A square is inscribed in a circle. If the area of the square is 9 in.2, what is the ratio of the circumference of the circle to the perimeter of the square?



Answer :

Step-by-step explanation:

**The ratio of the circumference of the circle to the perimeter of the square is 2π : 4, or π : 2.**

Since the area of the square is 9 square inches, the side length of the square is 3 inches. The perimeter of the square is therefore 4 * 3 = 12 inches.

The diameter of the circle is equal to the side length of the square, which is 3 inches. Therefore, the radius of the circle is 1.5 inches. The circumference of the circle is therefore 2π * 1.5 = 3π inches.

Therefore, the ratio of the circumference of the circle to the perimeter of the square is:

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3π inches / 12 inches = **2π : 4, or π : 2**

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