Question

3. Як зміниться периметр квадра- та, якщо його площу зменшити в 16 разів?​

Answer 1

Ответ:Р зменшиться у 4 рази

Пошаговое объяснение:Р²~S

Answer 2

Perimeter of a Square

The perimeter of a square is the sum of the lengths of all its sides. In a square, all sides are equal in length. Let's assume the length of one side of the square is s.

The formula to calculate the perimeter of a square is:

Perimeter = 4s

Changing the Area of a Square

The area of a square is the product of its length and width. In a square, since all sides are equal, the length and width are the same. Let's assume the length of one side of the square is s.

The formula to calculate the area of a square is:

Area = s^2

Changing the Area by a Factor of 16

If we decrease the area of a square by a factor of 16, it means we are reducing the area to 1/16th of its original value. Mathematically, this can be represented as:

New Area = Original Area / 16

Let's substitute the formula for the area of a square into this equation:

s^2 / 16 = New Area

Relationship between Perimeter and Area

To determine how the perimeter changes when the area is reduced by a factor of 16, we need to find the new length of one side of the square. Let's solve the equation above for s:

s^2 / 16 = New Area

Multiplying both sides of the equation by 16:

s^2 = 16 * New Area

Taking the square root of both sides:

s = √(16 * New Area)

Now that we have the new length of one side of the square, we can calculate the new perimeter using the formula:

New Perimeter = 4 * s

Example Calculation

Let's assume the original area of the square is 100 square units. If we decrease the area by a factor of 16, the new area would be:

New Area = 100 / 16 = 6.25 square units

Substituting this value into the equation for the new length of one side:

s = √(16 * 6.25) = √100 = 10 units

Finally, substituting the new length of one side into the formula for the new perimeter:

New Perimeter = 4 * 10 = 40 units

Therefore, if we decrease the area of a square by a factor of 16, the new perimeter will be 40 units.

Conclusion

When the area of a square is reduced by a factor of 16, the new perimeter can be calculated by finding the square root of 16 times the new area and multiplying it by 4. In the example provided, the original area of 100 square units was reduced to 6.25 square units, resulting in a new perimeter of 40 units.