Final answer:
The area of the larger square with side length 8 inches is four times that of the smaller square with a side length of 4 inches.
Step-by-step explanation:
The problem at hand involves comparing the areas of two squares, where one square has dimensions that are twice that of the other. To determine the area of the larger square, we first identify the scale factor and apply it to the dimensions of the smaller square. Given that the side length of the smaller square is 4 inches, the side length of the larger square is calculated as follows:
4 inches × 2 = 8 inches.
Next, we find the area of both squares. The area of the smaller square is:
4 inches × 4 inches = 16 square inches.
For the larger square, the area is:
8 inches × 8 inches = 64 square inches.
When comparing the two areas, we can establish a ratio. The area of the larger square is 64 square inches, and the area of the smaller square is 16 square inches, resulting in a ratio of 4:1. Hence, the area of the larger square is four times the area of the smaller square.