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triaglelover92
22. A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the area of the circle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square. (3 points)
let the length of each side of square is S area of circle = S^2 as the diameter of the circle is equal to the side length of the square thus the length of its radius become S/2 area of circle = pi (S/2)^2 can you find the ratio now??
let the side length of the square be x the radius of the circle is x/2 so the ratio of areas square to circle is \[x^2 : \pi (\frac{x}{2})^2\] or \[x^2 : \pi \frac{x^2}{4}\] it can be simplified by dividing both sides of the ratio by x^2 which gives \[1:\frac{\pi}{4}\] hope this makes sense.
So basically the ratio = 4/pi