Final answer:
The area of the larger square with side lengths twice as long as the smaller square's is four times greater, with a scale factor of 2 and an area ratio of 4 to 1.
Step-by-step explanation:
The student is asked to compare the area of two squares where one has side lengths twice as long as the other. To find the scale factor, we note that the dimensions of the second square are twice those of the first square. If the first square has side lengths of 4 inches, then the second square will have side lengths of 4 inches × 2 = 8 inches. To compare the areas, we square the side lengths. The area of the smaller square is 4 inches × 4 inches = 16 square inches. The area of the larger square is 8 inches × 8 inches = 64 square inches. Therefore, the ratio of the areas is 64 square inches to 16 square inches, or 4 to 1, meaning the larger square has an area four times greater than the smaller square.