Final answer:
The perimeter of a square with a side length 'a' is 4a. When comparing the areas of two squares where one has side length twice as much as the other, the area of the larger square is four times greater than the smaller one. For a rectangle with different length and width, the perimeter is the sum of twice the length plus twice the width.
Step-by-step explanation:
The perimeter of a rectangle or a square is the total distance around the figure. For a rectangle, the perimeter P is calculated by the formula P = 2l + 2w, where l is the length and w is the width. For a square, where all sides are equal (let's call the side length 'a'), the perimeter is P = 4a.
To compare the two areas, consider that the area of a square is calculated by squaring the side length (a²). If a square has a side length of 4 inches and the other square has a side length that is twice as much (8 inches), then the area of the larger square is 8² = 64 square inches, and the area of the smaller square is 4² = 16 square inches. Therefore, the larger square's area is 64/16 = 4 times larger than that of the smaller square.
Referring to a rectangle with a length of 39.2 meters and a width of 17.5 meters, its perimeter would be P = 2×39.2 + 2×17.5, which calculates to 113.4 meters.