Question

Длина окружности, описанной около квадрата, равно 8П см. Найдите периметр квадрата.

Answer 1

Длина окружности c=2*пи*R
2R = d (диаметр окружности описанной около квадрата = диагонали квадрата)
d=c / 2*пи = 8 см . Диагональ квадрата со стороной а = а корней из 2. Значит отсюда следует , что сторона квадрата = 4 корня из 2 .
P = 4*a = 4*4 корня из 2 = 16 корней из 2 

Answer 2

Perimeter of a Square Inscribed in a Circle

To find the perimeter of a square inscribed in a circle, we need to use the information given about the circumference of the circle.

The problem states that the length of the circumference of the circle is equal to 8π cm. We can use this information to find the radius of the circle, which will help us determine the side length and perimeter of the square.

Let's break down the solution step by step:

1. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. 2. In this case, the circumference is given as 8π cm. So we have 8π = 2πr. 3. We can cancel out the π on both sides of the equation, which gives us 8 = 2r. 4. Dividing both sides of the equation by 2, we get r = 4 cm. 5. The radius of the circle is 4 cm, which is also the distance from the center of the circle to any of its vertices. 6. In a square inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. 7. The diagonal of a square can be found using the formula d = a√2, where d is the diagonal and a is the side length of the square. 8. In this case, the diagonal is equal to the diameter of the circle, which is 2r = 2 * 4 = 8 cm. 9. Using the formula for the diagonal, we have 8 = a√2. 10. Dividing both sides of the equation by √2, we get a = 8/√2 = 4√2 cm. 11. The side length of the square is 4√2 cm. 12. The perimeter of a square is given by the formula P = 4a, where P is the perimeter and a is the side length of the square. 13. Substituting the value of a, we have P = 4 * 4√2 = 16√2 cm.

Therefore, the perimeter of the square is 16√2 cm.