Answer: C. $80$

Explanation:1. Convert the equation of the circle to standard form $(x-h)^2 + (y-k)^2 = r^2$ by completing the square: The given equation is $x^2-4x+y^2-8y-80=0$. Group x terms and y terms: $(x^2-4x) + (y^2-8y) = 80$ Complete the square for x terms: $x^2-4x$. Take half of the coefficient of x ($-4/2 = -2$) and square it ($(-2)^2 = 4$). Add $4$ to both sides. $(x^2-4x+4) + (y^2-8y) = 80+4$ Complete the square for y terms: $y^2-8y$. Take half of the coefficient of y ($-8/2 = -4$) and square it ($(-4)^2 = 16$). Add $16$ to both sides. $(x^2-4x+4) + (y^2-8y+16) = 80+4+16$ Rewrite as squared binomials: $(x-2)^2 + (y-4)^2 = 100$

2. Identify the radius of the circle: The standard form is $(x-h)^2 + (y-k)^2 = r^2$. From our equation $(x-2)^2 + (y-4)^2 = 100$, we have $r^2 = 100$. So, the radius $r = \sqrt{100} = 10$.

3. Relate the circle inscribed in a square to the square's dimensions: If a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. Diameter $d = 2 \times r = 2 \times 10 = 20$. So, the side length of the square (let's call it $s\_{sq}$) is $s\_{sq} = 20$.

4. Calculate the perimeter of the square: The perimeter of a square is $4 \times \text{side length}$. Perimeter = $4 \times s\_{sq} = 4 \times 20 = 80$.

5. Check the solution with the options: The calculated perimeter is $80$. This matches option [C].

6. Conclusion: The perimeter of the square is $80$.