Question

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 1

π√2 : 4

Explanation:

if area of square is 9, each side = 3.

radius of circle = √[(3/2)² + (3/2)²]

= (3√2)/2.

Diameter = 2 X radius = 3√2.

Circumference = π X D

= 3π√2

perimeter of square = 3 + 3 + 3 + 3 =12.

ratio of circumference to perimeter is

3π√2 : 12

= π√2 : 4