Question

Периметр квадрата 20 см знайти радіус кола вписаного в квадрат і описаного навколо квадрата

Answer 1

Ответ:

10(Вписаний) 20(описаний)

Объяснение:

Так як P(квадр) 20 см

Тоді ми знаемо шо коло вписано в квадрат

тоді діаметр буде 20см

d(діаметр)/r(радіус)

отже 20/2=10

А описаного буде дорівнювати 20

Answer 2

Perimeter of a Square

To find the radius of the circle inscribed in a square and the circle circumscribing the square, we need to know the perimeter of the square.

The perimeter of a square is the sum of all its sides. Let's assume the perimeter of the square is 20 cm.

Radius of the Inscribed Circle

The radius of the circle inscribed in a square is equal to half the length of the side of the square. In this case, since we know the perimeter of the square is 20 cm, we can find the length of each side by dividing the perimeter by 4 (since a square has four equal sides).

Let's calculate the length of each side of the square:

20 cm ÷ 4 = 5 cm

Therefore, the length of each side of the square is 5 cm.

The radius of the circle inscribed in the square is equal to half the length of each side of the square:

Radius = 5 cm ÷ 2 = 2.5 cm.

Radius of the Circumscribed Circle

The radius of the circle circumscribing the square is equal to half the length of the diagonal of the square. To find the diagonal of the square, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In a square, the diagonal is the hypotenuse of a right triangle formed by two sides of the square. Since the sides of the square are equal, the right triangle is an isosceles right triangle.

Let's calculate the length of the diagonal of the square:

Using the Pythagorean theorem: a^2 + a^2 = c^2, where a is the length of each side of the square and c is the length of the diagonal.

5 cm^2 + 5 cm^2 = c^2 25 cm^2 + 25 cm^2 = c^2 50 cm^2 = c^2 c = √50 cm ≈ 7.07 cm.

Therefore, the length of the diagonal of the square is approximately 7.07 cm.

The radius of the circle circumscribing the square is equal to half the length of the diagonal of the square:

Radius = 7.07 cm ÷ 2 = 3.54 cm.

To summarize: - The radius of the circle inscribed in the square is approximately 2.5 cm. - The radius of the circle circumscribing the square is approximately 3.54 cm.

Please note that the calculations provided are based on the assumption that the perimeter of the square is 20 cm. If the perimeter is different, the results will vary accordingly.