Final answer:
The larger square, when scaled up by a factor of 2, has side lengths of 8 inches and an area four times larger than the smaller square with 4-inch side lengths. For the specific problem of the pool, the area that needs to be covered after removing the corners is 64 square feet.
Step-by-step explanation:
Understanding the Area of Scaled Squares
The original square has side lengths of 4 inches. When scaled up by a factor of 2, the new square will have side lengths of 8 inches. To compare the area of the larger square to the area of the smaller square, we square the side lengths. The small square has an area of 4 inches × 4 inches = 16 square inches. The larger square has an area of 8 inches × 8 inches = 64 square inches. This shows that the area of the larger square is 4 times larger than the area of the smaller square, consistent with the rule that the ratio of the areas of similar figures is the square of the scale factor.
Applying this logic to the original question of a square with cutout corners: If the original square is 12 feet on each side, four 2 feet by 2 feet squares are removed from each corner, leaving an area that needs to be covered as (12 feet - 2 feet × 2) × (12 feet - 2 feet × 2) = 64 square feet.