Final answer:
The correct answer is that side AD is three times larger than side AB (AD = 3AB). Without figures, it is challenging to compare areas A1, A2, and A3, and we must know the scale factor for Marta's squares to determine the relative areas.
Step-by-step explanation:
The question pertains to a rectangle on a coordinate system and compares the lengths of its sides, given that one side is three times larger than another. When it mentions that side AD is three times larger than side AB, it means AD = 3AB (option a). To clarify, if AB is x units long, then AD would be 3x units long, emphasizing the length relationship between sides AD and AB.
In another part, the question seems to be comparing the areas of shapes A₁, A₂, and A3. Without additional context or a figure, it's difficult to provide an accurate comparison, but generally, if the areas are supposed to be the same, the answer would be option b: A₁ = A₂ = A3. If one is larger or smaller, different options (c or d) would be correct based on provided values.
Finally, Marta's square problem involves understanding how the area of a square changes when its dimensions are scaled. When the side length of a square is doubled, the area becomes four times larger because area is proportional to the square of the side length (A = side²).