did perimeter and area of rectangles change in the same way it does for squares explain your thinking
This doesn't seem to be a complete problem.
Which perimeter and area?
Pearson Education
To answer your question, we first need to understand how perimeter and area are calculated for rectangles and squares.
The perimeter of any polygon is the total length of its boundary. In the case of a rectangle, we add the lengths of all four sides to find the perimeter. If the rectangle has side lengths "length" and "width," the perimeter (P) would be calculated as: P = 2(length + width).
The area of a rectangle is the measure of the surface inside the shape. For a rectangle, it is calculated by multiplying the length by the width. If the rectangle has side lengths "length" and "width," the area (A) would be calculated as: A = length × width.
Now, let's compare the changes in perimeter and area for rectangles and squares.
In a square, all four sides are equal in length. Therefore, if we increase or decrease the side length, the perimeter changes in the same way. For example, if we double the side length of a square, the perimeter would also double because all four sides are affected equally.
Likewise, since the area of a square is calculated by multiplying the side length by itself (A = side length × side length), if we increase or decrease the side length, the area changes in the same way. If we double the side length, the area would increase by a factor of four because we are multiplying two sides that are both two times larger.
Similarly, for rectangles, if we change the length or width, the perimeter changes in the same way, because each side contributes to the overall boundary. Additionally, the area changes based on the product of the length and width. So if we double both the length and width, the area would increase by a factor of four.
In summary, for both squares and rectangles, the changes in perimeter and area are proportional and happen in the same way as we modify the side lengths or dimensions.