Ratio between the sides of two squares: 2:5

To find the ratio between the perimeter and area of two squares with side lengths in a ratio of 2:5, we can follow these steps:

1. Understanding the Problem:
- We have two squares with side lengths in a ratio of 2:5.
- Let's assume the side lengths of the squares are 2x and 5x, respectively, where x is a common factor.
- We need to find the ratio between the perimeter and area of these squares.

2. Calculating the Perimeter:
- The perimeter of a square is given by the formula P = 4s, where s is the length of a side.
- Let's calculate the perimeters of the two squares:
- The perimeter of the first square with side length 2x is P1 = 4(2x) = 8x.
- The perimeter of the second square with side length 5x is P2 = 4(5x) = 20x.

3. Calculating the Area:
- The area of a square is given by the formula A = s^2, where s is the length of a side.
- Let's calculate the areas of the two squares:
- The area of the first square with side length 2x is A1 = (2x)^2 = 4x^2.
- The area of the second square with side length 5x is A2 = (5x)^2 = 25x^2.

4. Finding the Ratio:
- Now, let's find the ratio between the perimeters and the areas of the two squares:
- The ratio of the perimeters: P1:P2 = 8x:20x = 2:5.
- The ratio of the areas: A1:A2 = 4x^2:25x^2 = 4:25.

5. Explanation:
- The ratio between the perimeters of the two squares is 2:5, which means the second square has a perimeter that is 2.5 times greater than the first square.
- The ratio between the areas of the two squares is 4:25, which means the second square has an area that is 6.25 times greater than the first square.
- This shows that as the ratio of the side lengths increases, the ratio between the perimeters and areas also increases.
- The ratio of the perimeters is smaller than the ratio of the areas, indicating that the increase in side length has a greater impact on the area compared to the perimeter.

In summary, the ratio between the perimeters of the two squares is 2:5, and the ratio between the areas is 4:25. The increase in side length has a greater impact on the area compared to the perimeter.

To find the ratio between the perimeters of two squares, we can simply compare the lengths of their sides. Let's assume the side lengths of the squares are 2x and 5x, respectively.

(a) Perimeter ratio:
The perimeter of a square is given by the formula P = 4s, where s is the length of a side.

For the first square with side length 2x, its perimeter would be P1 = 4(2x) = 8x.
For the second square with side length 5x, its perimeter would be P2 = 4(5x) = 20x.

Therefore, the ratio between their perimeters is 8x:20x, which simplifies to 2:5.

(b) Area ratio:
The area of a square is given by the formula A = s^2, where s is the length of a side.

For the first square with side length 2x, its area would be A1 = (2x)^2 = 4x^2.
For the second square with side length 5x, its area would be A2 = (5x)^2 = 25x^2.

Therefore, the ratio between their areas is 4x^2:25x^2, which simplifies to 4:25.

So, the ratio between the perimeters is 2:5, and the ratio between the areas is 4:25.