Final answer:
The flower garden is larger than the vegetable garden because it is 1 1/4 times the area. For the scale drawing, the actual width of a flower garden would be 72 inches if the scale is 1:12. A square with side length double that of another square has four times the area of the smaller square.
Step-by-step explanation:
Marcia's flower garden is 1 1/4 times the area of her vegetable garden. When a dimension is multiplied by a factor greater than 1, the resulting area is larger than the original. Hence, the area of the flower garden is larger than that of the vegetable garden.
For the flower garden scale drawing question from LibreTexts™, if the width on the plan is 6 inches and the scale is 1:12, this means that every inch on the plan represents 12 inches in reality. Therefore, the actual width would be 6 inches × 12 which is 72 inches.
When Marta has a square with side length of 4 inches and then creates a similar square with side lengths twice as long, the side length of the larger square is 8 inches. Since the area of a square is side length squared, the smaller square's area is 16 square inches (4 inches × 4 inches), while the larger square's area is 64 square inches (8 inches × 8 inches). Comparing the areas, the larger square is four times the area of the smaller one (64 divided by 16 equals 4).