Answer:
48 in
Step-by-step explanation:
The diagonal of the inscribed square equals the diameter of the circle.
1. Calculate the diagonal of the square
d = 2r = 2 × 6√2 in =12√2 in
2. Calculate the side of the square
∆ACB is an isosceles right triangle.
We can use Pythagoras' Theorem to calculate the length of a side s.
[tex]\begin{array}{rcl}s^{2} + s^{2} & = & (12\sqrt{2})^{2}\\2s^{2} & = & 144 \times 2\\s^{2} & = & 144\\s & = & \text{12 in}\\\end{array}[/tex]
3. Calculate the perimeter of the square
P = 4s = 4 × 12 in = 48 in
The perimeter of the square is 48 in.
