Question

A square of side length x just fits inside a circle. Find the exact circumference of

the circle in terms of x.

Answer 1

The relationship between the side length of a square and the diameter of a circle that just fits inside it can be expressed as follows:

x = diameter of the circle / √2

Since the circumference of a circle is equal to π times the diameter, the circumference of the circle in terms of x can be found by solving for the diameter and then multiplying by π:

diameter of the circle = x * √2

circumference of the circle = π * diameter of the circle = π * (x * √2) = 2 * π * x * (1 / √2) = 2 * π * x * √2.

So, the exact circumference of the circle is 2 * π * x * √2 in terms of x