Final answer:
Both Pauline and Rene could have arrived at different but correct areas for a rectangle if they were given different dimensions or used different units of measurement when performing their calculations.
Step-by-step explanation:
The scenario where Pauline calculated an area of a rectangle to be 216 and Rene calculated it to be 1.5 and yet both answers were deemed correct is intriguing. To understand how this could occur, we need to consider multiple factors such as scale, proportions, and units of measurement. When calculating the area of a rectangle, the standard method involves multiplying the length by the width. If Pauline and Rene received different results but were still correct, it suggests that while the calculations themselves may have been done correctly, either the dimensions given to each student or the units of measurement used were different.
Option C states that they were given different dimensions, which would naturally result in different areas even when the correct arithmetic operations are used. Option D suggests a difference in units of measurement; for instance, if Pauline measured in inches and Rene measured in feet, their calculations could yield correct but numerically different areas due to conversion factors.
The explanation lies in understanding the importance of dimensions and units when calculating areas and forming proportions for scale drawings or models. To solidify this concept, consider the example of Marta's squares, where the larger square has dimensions twice that of the smaller square. The area of the larger square is four times that of the smaller square because the side length has been doubled, and area is a function of the side length squared.