Final answer:
The dimensions of the rectangle with the maximum area that can be inscribed in the given circle are 6 units by 6 units, making it a square with an area of 36 square units.
Step-by-step explanation:
The question is to find the dimensions of a rectangle with the maximum area that can be inscribed in a circle with the equation x^2 + y^2 = 9. The equation represents a circle with radius 3 (since r2 = 9, r = 3), and thus a diameter of 6.
Since the rectangle is inscribed within the circle, its length and width will correspond to diameters along the x and y axes, respectively. The maximum area for a rectangle is achieved when the rectangle is actually a square, with each side equal to the diameter of the circle.
The area of the square can be described as a2, where a is the side length. In this case, the maximum area inscribed rectangle (which is a square) will have side lengths of 6, the diameter of the circle. Hence, the maximum area of the rectangle will be 62 = 36 square units.