Step-by-step explanation:
Let the side of square be a and radius of circle be r.
The perimeter of a particular square and the circumference of a particular circle are equal.
Perimeter of square = 4 x a = 4a
Circumference of circle = 2πr
Given that
4a = 2πr
[tex]a=\frac{\pi r}{2}[/tex]
We need to find the ratio of the area of the square to the area of the circle.
Area of the square = a²
Area of the circle = πr²
[tex]\texttt{Ratio of area of the square to the area of the circle =}\frac{a^2}{\pi r^2}\\\\\texttt{Ratio of area of the square to the area of the circle =}\frac{\left ( \frac{\pi r}{2}\right )^2}{\pi r^2}\\\\\texttt{Ratio of area of the square to the area of the circle = }\frac{\pi}{4}[/tex]
Ratio of area of the square to the area of the circle = π/4
