Final Answer:
A) The measures for a perfect square are not proportional in terms of the length of a side and the perimeter.
B) The measures for a perfect square are not proportional in terms of the length of a side and the area.
Step-by-step explanation:
For a perfect square with a side length labeled as 's,' the perimeter (P) is given by the formula P = 4s, where each side contributes to the total perimeter. In terms of proportionality, as the length of a side (s) increases, the perimeter (P) increases linearly, following a direct proportionality. However, this doesn't meet the definition of proportionality, where a constant ratio should exist between the two measures.
Similarly, for the area (A) of a perfect square, the formula is A = s^2. In this case, as the side length (s) increases, the area (A) increases exponentially, not maintaining a constant ratio. Therefore, the measures for a perfect square are not proportional in terms of the length of a side and the area.
Understanding proportionality is crucial in mathematical relationships, and in the context of geometric figures like squares, recognizing how changes in one measure affect another provides insights into their properties and behaviors. In summary, the measures for a perfect square, whether it's the length of a side and the perimeter or the length of a side and the area, are not proportional.