Final answer:
By doubling the side length of a square from 4 inches to 8 inches, the area increases by a scale factor of 4, resulting in the larger square having an area four times greater than the smaller square.
Step-by-step explanation:
The question presents a scenario involving two squares where the second square has dimensions twice those of the first square. Since Marta's original square has a side length of 4 inches, we can calculate the side length of the larger square by doubling that measurement. This gives us:
-
- Side length of larger square = 4 inches × 2 = 8 inches
To compare the area of the two squares, we square the side lengths:
-
- Area of the smaller square = 4 inches × 4 inches = 16 square inches
-
- Area of the larger square = 8 inches × 8 inches = 64 square inches
The area of the larger square is four times that of the smaller square because when side lengths are doubled, the area increases by a scale factor of the square of the multiplier, which in this case is 2² = 4.