Final answer:
The two rectangles, one measuring 12 inches by 8 inches and the other 18 inches by 12 inches, are proportional because the simplified ratios of their corresponding sides' lengths and widths are equivalent, both being 2/3.
Step-by-step explanation:
To determine whether the two given rectangles are proportional, we need to compare the ratios of their corresponding sides. If the ratios are equivalent, then the rectangles are proportional. Let's set up the proportions for the length ratios and width ratios.
The first rectangle is 12 inches by 8 inches, and the second rectangle is 18 inches by 12 inches. To form the proportion for the lengths, we compare 12 inches to 18 inches, and for the widths, we compare 8 inches to 12 inches:
- Length Proportion: 12 inches / 18 inches
- Width Proportion: 8 inches / 12 inches
By simplifying both ratios, we see that:
- Length Proportion: 12/18 = 2/3
- Width Proportion: 8/12 = 2/3
Since both proportions have the same simplified ratio of 2/3, we can conclude that the two rectangles are indeed proportional.