Final answer:
To find the length of the rectangle's longer sides, one must calculate the distance between two top or bottom vertices. Applying the distance formula, the length is found to be 15 units.
Step-by-step explanation:
The student's question is about finding the length of the longer sides of a rectangle given four vertices. The rectangle's vertices provided are (-3, -4), (-3, 7), (12, -4), and (12, 7). To find the length of the longer sides, we can calculate the distance between either the top two vertices or the bottom two, since these will represent the longer sides of the rectangle. Using the distance formula d = √((x_2 - x_1)^2 + (y_2 - y_1)^2), we apply it to, for example, the top two vertices (-3, 7) and (12, 7), since the y-coordinates are the same, the formula simplifies to just the difference in x-coordinates, which is 12 - (-3) = 15. Hence, the length of each of the longer sides of the rectangle is 15 units.