Question

Периметр квадрата 32см. Сторону этого квадрата увеличили в 2 раза. На сколько квадратных сантиметров увеличилась площадь квадрата? Задачу решать нужно в таких формах: Дано: Решение:

Answer 1

Дано: квадрат
P=32см
Решение:
32÷4=8 (cм)-сторона квадрата
8×2=16 (см)-увеличеная сторона квадрата
16×16=256(см²) - площадь увеличенного квадрата
8×8=64(см²)- площадь начального квадрата
256÷64=4 
Ответ: в 4 раза увеличилась площадь

Answer 2

Problem Analysis

We are given the perimeter of a square, which is 32 cm. We need to find the increase in the area of the square when its side is increased by a factor of 2.

Solution

To solve this problem, we need to find the side length of the original square and the side length of the new square. Then we can calculate the areas of both squares and find the difference.

Let's denote the side length of the original square as x. The perimeter of a square is given by the formula: perimeter = 4 * side length. So we have the equation:

4 * x = 32

Simplifying the equation, we find:

x = 32 / 4 = 8 cm

Therefore, the side length of the original square is 8 cm.

The side length of the new square is given as twice the side length of the original square, so:

new side length = 2 * 8 = 16 cm

To find the area of a square, we use the formula: area = side length * side length. Therefore, the area of the original square is:

original area = 8 * 8 = 64 cm^2

And the area of the new square is:

new area = 16 * 16 = 256 cm^2

The increase in the area of the square is the difference between the new area and the original area:

increase in area = new area - original area = 256 - 64 = 192 cm^2

Therefore, the area of the square increased by 192 square centimeters.

Answer

The area of the square increased by 192 square centimeters when the side of the square was increased by a factor of 2.