Question

Длина окружности, вписанной в квадрат равна 12пи см. Найдите сторону квадрата и радиус описанной окружности

Answer 1

Длина окружности равна 2ПиR Отсюда R=6 см, а сторона квадрата 12 см. Радиус описанной окружности равен половине диагонали квадрата и равен - 12(корень из 2)

Answer 2

Finding the Side Length of the Square and the Radius of the Circumscribed Circle

To find the side length of the square and the radius of the circumscribed circle, we can use the information given about the circumference of the circle.

Let's denote the side length of the square as s and the radius of the circumscribed circle as r.

The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius.

In this case, the circumference of the circle is given as 12π cm. Therefore, we can write the equation as:

12π = 2πr

Simplifying the equation, we can cancel out the π on both sides:

12 = 2r

Dividing both sides of the equation by 2, we get:

6 = r

So, the radius of the circumscribed circle is 6 cm.

To find the side length of the square, we can use the relationship between the side length and the radius of the circumscribed circle. In a square, the diagonal is equal to twice the radius of the circumscribed circle.

The diagonal of a square can be found using the Pythagorean theorem: d^2 = s^2 + s^2, where d is the diagonal and s is the side length.

In this case, the diagonal is equal to 2 times the radius, so we have:

d = 2r = 2 * 6 = 12 cm

Using the Pythagorean theorem, we can find the side length of the square:

12^2 = s^2 + s^2

Simplifying the equation, we get:

144 = 2s^2

Dividing both sides of the equation by 2, we have:

72 = s^2

Taking the square root of both sides, we find:

s = √72 = 6√2 cm

Therefore, the side length of the square is 6√2 cm.

To summarize: - The radius of the circumscribed circle is 6 cm. - The side length of the square is 6√2 cm.