Final answer:
The expression for the side length of the square is x + 2 meters. When scaling the dimensions of a square by a factor of two, the area of the larger square becomes four times the area of the smaller square.
Step-by-step explanation:
The area of a square is calculated by squaring the length of one side, which is denoted as side length x. For a square with an area of x^2 + 4x + 4 square meters, we can understand this as a perfect square trinomial. This expression can be factored into (x + 2)^2, revealing that the side length of the square is x + 2 meters. Therefore, the expression representing the length of one side of the square is x + 2.
If Marta has a square with a side length of 4 inches and another square with dimensions that are twice as large, the side of the larger square will be 8 inches. The area of a square is the side length squared, so the larger square will have an area of 64 square inches, which is four times larger than the smaller square with an area of 16 square inches. This is because when the side lengths are doubled, the area increases by a factor of two squared, which is four.