Final answer:
Rectangles are considered similar if they have congruent corresponding angles and proportional corresponding sides. The ratio of the sides must be constant for similarity, regardless of whether the perimeters are different. In the case of squares with side lengths in a fixed ratio, the area of the larger square is the square of that ratio times the area of the smaller square.
Step-by-step explanation:
The question of whether rectangles are similar can be answered by looking at their corresponding angles and the ratios of their corresponding sides. Similar figures, including rectangles, must have corresponding angles that are congruent and the ratios of corresponding sides that are proportional. It is not enough for rectangles to have equal side lengths, nor does a difference in perimeter rule out similarity.
To determine if two rectangles are similar, one can look at option c) which states Yes, because their corresponding angles are congruent. This is a characteristic feature of similar rectangles. Even when the side lengths are not equal, as long as the ratio of the sides is constant, and the angles are congruent, the rectangles are indeed similar.
As for the concept of area in relation to similarity, when dealing with square figures, if one square has side length twice as much as the other, then its area will be four times greater because the area of a square is calculated as the side length squared. Therefore, if Marta has a square with a side length of 4 inches and another square with dimensions that are twice the first square, the area of the larger square would be 16 times the area of the smaller square, because the side length is squared to get the area (Area = side²).