Final answer:
Without the scale factor between rectangles S and T, we cannot provide the exact area of rectangle T. However, the areas of similar rectangles are proportional to the square of the scale factor. As illustrated by Marta's squares, if one dimension doubles, the area becomes four times larger.
Step-by-step explanation:
To determine the area of rectangle T, given that rectangles S and T are similar, and the area of rectangle S is 45, we need additional information. Specifically, we need to know the scale factor between rectangle S and T. Without this information, we can't calculate the exact area of rectangle T. However, we can state that the area of similar rectangles is proportional based on the square of the scale factor.
Marta has a square with a side length of 4 inches, and a larger similar square with dimensions that are twice as large. Since the area of a square is equal to the side length squared, the area of the larger square would be "4 inches x 2" squared, which is "8 inches" squared, resulting in 64 square inches. This is 4 times larger than the area of the smaller square, which is 16 square inches (4 inches squared).
Therefore, following this rule, the ratio of the areas of the similar figures is the square of the scale factor. If rectangle T were twice as large as rectangle S in each dimension (like in Marta's square example), then the area of rectangle T would be 4 times that of rectangle S, which would be 45 x 4 = 180.