Final answer:
The larger square, with side lengths twice as long as the smaller square, has an area four times as large. The ratio of their areas is 4, showcasing that the ratio of areas of similar figures is the square of the scale factor.
Step-by-step explanation:
The problem provided is one of geometry, in which the student is asked about the relationship between the dimensions of two squares and their areas. Given that Marta has one square with a side length of 4 inches and another that has dimensions twice as large, we are to determine how their areas compare.
To solve this, we calculate the area of each square. The area of the smaller square is simply the square of the side length, which is 4 inches x 4 inches = 16 square inches. The larger square has sides twice the length, so 8 inches x 8 inches = 64 square inches. Comparing the areas, we see that the larger square's area is four times the smaller square's.
The ratio of the area of the larger square to the smaller square is 64 square inches / 16 square inches = 4. This illustrates the rule that when comparing the areas of similar figures, the ratio of their areas is the square of the scale factor.