A circle in the xy-plane is defined by the equation (x - 2)^2 + (y + 5)^2 = 81. This circle is inscribed in a square wh…

The standard equation of a circle in the xy-plane is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. For the given equation, (x - 2)² + (y + 5)² = 81, we can see that r² = 81. Taking the square root of both sides gives a radius of r = 9. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. The diameter is twice the radius, so the diameter is 2 · 9 = 18.

Therefore, the side length of the square is 18. The perimeter of a square is calculated as 4 times the side length.

So, the perimeter of this square is 4 · 18 = 72.

Choice A is incorrect; 18 is the side length of the square, not the perimeter.

Choice B is incorrect because 36 would be the perimeter if the radius (9) were mistakenly used as the side length.

Choice D is incorrect because 324 is the area of the square (18 · 18), not the perimeter.