Final answer:
The correct answer is option a, which presents the square room with an area of x^2 square feet and the rectangle room with dimensions that correspond to (x-4)(x+5) square feet, both illustrating equal areas as described in the problem.
Step-by-step explanation:
To find the area of each room, we must set up equations based on the description. Let the side length of the square room be x feet. This means the area of the square room is x^2 square feet. The rectangle room is 4 feet narrower and 5 feet longer than the square room, so its dimensions are (x - 4) feet wide and (x + 5) feet long. Since the areas of the rooms are equal, the area of the rectangle room can also be expressed as (x - 4)(x + 5) square feet.
Using Marta's squares as an example, if a square has a side length of 4 inches, it has an area of 16 square inches. A similar square with side lengths twice as long, or 8 inches, will have an area of 64 square inches. This exemplifies the rule that the area of the larger square is 4 times larger than the area of the smaller square, corresponding to the square of the scale factor (in this case, 2^2 = 4).
Therefore, the answer that accurately represents the areas of the two rooms is option a, which states: Square room: ( x^2 ) square feet, Rectangle room: (x-4)(x+5) square feet.