f the perimeter of a circle is equal to that of a square, then the ratio of their areas is

The perimeter of a circle is given by the formula 2πr, where r is the radius of the circle. The perimeter of a square is given by the formula 4s, where s is the side length of the square.

If the perimeters of the circle and the square are equal, we can set the two formulas equal to each other:

2πr = 4s => r = 2s/π

The area of a circle is given by the formula πr², and the area of a square is given by the formula s². Substituting r = 2s/π into the formula for the area of a circle, we get:

Area of circle = π(2s/π)² = 4s²/π

So, the ratio of the area of the circle to the area of the square is:

(4s²/π) : s² = 4/π : 1

Therefore, the ratio of the area of the circle to the area of the square is 4/π : 1, or approximately 1.273 : 1.