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The larger square's perimeter is 2 times larger than the smaller square's. The larger square's area is 4 times larger than the smaller square's. Both factors are related to the ratio of the corresponding sides of each square.

Step-by-step explanation:

The perimeter is simply the sum of all of the sides of a polygon. Therefore, the ratio of the perimeters of the squares will be equal to the ratio of the sides of the squares. The sides of the larger square are 2 times larger than that of the smaller square, therefore their ratio of perimeters is .

The area of a square is given by , where is the side of the square. Since we're squaring a side, we should square the sides' ratio to find the ratio of the areas: .

Both of these ratios are directly related to the proportion each side is in between the smaller and larger square. Therefore, if you know the ratio of sides between two squares, you should be able to find the ratio of the two squares' area and perimeter without actually finding the value of the area and perimeter.

Conceptually: