Final answer:
The maximum perimeter of the square is 20√2 cm.
Step-by-step explanation:
To find the maximum perimeter of a square that can fit inside a circle of radius 5 cm, we need to determine the side length of the square. The diagonal of the square will be equal to the diameter of the circle, which is 10 cm. Using the Pythagorean theorem, we can calculate the length of each side of the square.
Let's assume the side length of the square is 'a'. Using the Pythagorean theorem, we have:
a^2 + a^2 = 10^2
2a^2 = 100
a^2 = 50
a = √50 = 5√2
The maximum perimeter of the square is 4 times the side length, so the maximum perimeter is 4 x 5√2 = 20√2 cm.