Final answer:
Using the concept of scale factor, it's determined that the length of PQ in the larger parallelogram is 40 inches, since it's a scaled-up version of the smaller parallelogram by a factor of 2.5.
Step-by-step explanation:
The question is asking to find the length of line PQ for two similar parallelograms. To solve this problem, we need to use the concept of scale factor. Since the parallelograms are similar, their corresponding sides are in proportion.
In this case, we are given that one of the sides of a smaller parallelogram is 12 inches and the corresponding side of the larger parallelogram is 30 inches. To find the scale factor, we can set up a proportion using these two side lengths. The scale factor is the ratio of a side length of the larger figure to the corresponding side length of the smaller figure. So, we have 30 inches / 12 inches = 2.5. This means that the larger parallelogram is scaled up by a factor of 2.5.
Now, we are also given that another side of the smaller parallelogram is 16 inches. To find the length of the corresponding side PQ of the larger parallelogram, we multiply the smaller side length by the scale factor: 16 inches * 2.5 = 40 inches. Hence, the correct answer is d) 40 inches.