Final answer:
When the dimensions of a square are doubled, the perimeter doubles, and the area increases by a factor of four. The side length of Marta's larger square is 8 inches, leading to a perimeter of 32 inches, and the area becomes 64 square inches.
Step-by-step explanation:
If the dimensions of a figure, such as a square, are doubled, then the perimeter of the figure also doubles. To understand this, let's consider an example where a square has a side length of 4 inches. If the dimensions are doubled, the side length becomes 4 inches x 2 = 8 inches. Since the perimeter of a square is 4 times the length of one side, the original square's perimeter is 4 x 4 inches = 16 inches, and the larger square's perimeter is 4 x 8 inches = 32 inches. Thus, when the side length is doubled, the perimeter also doubles.
The area of the larger square, however, increases by a factor of four (22 = 4) because area is a two-dimensional measure (side length squared). This is a common mistake to avoid: while the perimeter merely doubles, the area increases by a factor of four. In the case of the squares Marta has, the original area is 4 inches x 4 inches = 16 square inches, and the larger square's area is 8 inches x 8 inches = 64 square inches. Thus the area of the larger square is four times the area of the smaller square, and not double.