Final answer:
The area of the larger square is four times greater than the smaller square because when the side lengths are doubled, the area increases by a factor of the square of the scale factor (2² = 4).
Step-by-step explanation:
The question provided requires determining how the area of a larger square compares to a smaller square when the side length of the larger square is twice that of the smaller one.
Firstly, let's find the area of the smaller square. As given, the smaller square has a side length of 4 inches, thus:
Area of smaller square = side length × side length = 4 inches × 4 inches = 16 square inches.
For the larger square with each side being twice the length of the smaller square's side, which is 8 inches, the area will be:
Area of larger square = 8 inches × 8 inches = 64 square inches.
Therefore, the area of the larger square is four times the area of the smaller square because the scale factor for the area is the square of the scale factor for the dimensions (2² = 4).
Comparison of Areas:
To compare the two areas, we set up a ratio (larger area / smaller area):
64 square inches / 16 square inches = 4
This shows that the larger square's area is 4 times greater than the smaller square's area.