Final answer:
The perimeter of a square is four times its side length. For a larger square with side lengths doubled, the perimeter would double, and the area would quadruple, as the ratio of areas of similar figures is the square of the scale factor.
Step-by-step explanation:
Understanding the Perimeter and Area of Squares
When dealing with the perimeter of a square, we know that it is calculated by the formula f(s) = 4s, where s is the side length of the square. For a square with a side length of 4 inches, the formula gives us a perimeter of 16 inches. If we have a larger square with dimensions twice that of the first square, its side length would be 4 inches × 2 = 8 inches.
Now, let's consider the area of these squares. The area of a square is calculated by squaring its side length, so for the smaller square with a side length of 4 inches, the area would be 4 inches × 4 inches = 16 square inches. However, for the larger square with side of 8 inches, the area would be 8 inches × 8 inches = 64 square inches. Thus, the area of the larger square is four times the area of the smaller square, demonstrating that the ratio of areas of similar figures is the square of the scale factor.