Final answer:
To determine similarity, the ratios of the lengths and the widths of the two area rugs are compared and found to be equal, indicating that the rugs are similar. An example of scaling and area comparison is provided where a larger square, similar to a smaller one, has an area four times greater.
Step-by-step explanation:
To determine whether the two area rugs Roxanne saw at the mall are similar, we need to compare their ratios of corresponding sides, since similar figures have corresponding sides in the same ratio. The first rug measures 12 ft by 8 ft, and the second one measures 15.6 ft by 10.4 ft. To check if they are similar, we can divide the length of one rug by the length of the other and do the same for the width
12 ft / 15.6 ft = 0.7692 (approximately)
8 ft / 10.4 ft = 0.7692 (approximately)
Since the ratios of the lengths and the widths are the same, the rugs are similar.
Now, let's look at an example of scaling in similar figures:
Marta has a square with a side length of 4 inches. Using a scale factor of 2, the similar square has a side length of 4 inches * 2 = 8 inches. The area of the smaller square is 4 inches * 4 inches = 16 sq. in., while the area of the larger square is 8 inches * 8 inches = 64 sq. in.. To compare the two areas, we use a ratio: 64 sq. in. / 16 sq. in. = 4. This shows that the area of the larger square is 4 times greater than the area of the smaller square.