Question

6. : Во сколько раз увеличится периметр квадрата, если его площадь увеличилась в 9 раз? ​

Answer 1

P=4a

S=a²

S увеличилась в 9 раз

=>S = 9a² = (3a²)

Т.к площадь увеличилась в 3 раза, то и периметр увеличился в 3 раза

=> P= 4a × 3=12a

Ответ: P = 12a

           S = (3a)²

Answer 2

Ответ:

периметр квадрата больше плащади в 1.5 раза

следовательно 9*1.5=14.5

Answer 3

Если площадь квадрата увеличилась в 9 раз, то во сколько раз увеличится его периметр?

Understanding the Problem

To solve this problem, we need to find the relationship between the area and the perimeter of a square.

Solution

Let's assume the original side length of the square is x. The area of the square is given by x^2, and the perimeter is given by 4x.

If the area of the square increases by a factor of 9, then the new area is 9x^2. We need to find the new perimeter, which we'll call P'.

To find the new perimeter, we need to find the new side length of the square. We can do this by taking the square root of the new area: sqrt(9x^2) = 3x.

Now that we have the new side length, we can find the new perimeter by multiplying it by 4: P' = 4 * 3x = 12x.

Therefore, the new perimeter is 12 times the original perimeter.

Answer

The perimeter of the square will increase by a factor of 12 if its area increases by a factor of 9.

Explanation

Let's consider an example to illustrate this.

Suppose the original square has a side length of 2 units. The original area is 2^2 = 4 square units, and the original perimeter is 4 * 2 = 8 units.

If the area increases by a factor of 9, the new area is 9 * 4 = 36 square units.

To find the new side length, we take the square root of the new area: sqrt(36) = 6 units.

The new perimeter is then 4 * 6 = 24 units.

The new perimeter of 24 units is 12 times the original perimeter of 8 units, which confirms our earlier answer.

Example Calculation

Original area: 4 square units Original perimeter: 8 units New area: 36 square units New side length: 6 units New perimeter: 24 units

Note

Please note that the answer provided is based on the assumption that the increase in area is proportional to the increase in side length. This assumption holds true for squares, but may not be valid for other shapes.