Question

Стороны параллелограмма равны 16 см и 18 см, а угол между ними 30 градусов.  Найти периметр равновеликого квадрата.​

Answer 1

Ответ:

Объяснение:

1)проведём высоту BC, треугольник ABH - прямоугольный

2) BH = 32 cm так как катет лежащий против угла в 30 градусов равен половине гипотенузы

3) S параллелограмма = основание * высоту, основание AD = 18 cm, высота BH= 32 cm => S параллелограмма = 960 c

Answer 2

Calculating the Perimeter of an Equiangular Square

To find the perimeter of an equiangular square given the sides of a parallelogram, we can use the following steps:

1. Find the Length of the Diagonal of the Parallelogram: - The length of the diagonal of the parallelogram can be found using the given sides and the angle between them.

2. Use the Diagonal to Find the Side Length of the Square: - Once we have the length of the diagonal, we can use it to find the side length of the equiangular square.

3. Calculate the Perimeter of the Square: - Finally, we can use the side length of the square to calculate its perimeter.

Let's proceed with these steps.

Finding the Length of the Diagonal of the Parallelogram

The length of the diagonal of the parallelogram can be found using the given sides and the angle between them.

Given: - Side 1 of the parallelogram = 16 cm - Side 2 of the parallelogram = 18 cm - Angle between the sides = 30 degrees

Using the law of cosines, we can find the length of the diagonal (d) of the parallelogram: ``` d = sqrt(16^2 + 18^2 - 2*16*18*cos(30)) ``` Calculating the value of d: ``` d ≈ 21.563 cm ```

Use the Diagonal to Find the Side Length of the Square

Since the square is equiangular, the diagonal of the square is related to its side length (s) by the formula: ``` d = s * sqrt(2) ``` Solving for s: ``` s = d / sqrt(2) s ≈ 15.263 cm ```

Calculate the Perimeter of the Square

The perimeter of the equiangular square can be calculated using the formula: ``` Perimeter = 4 * s ``` Substituting the value of s: ``` Perimeter ≈ 4 * 15.263 Perimeter ≈ 61.052 cm ``` The perimeter of the equiangular square is approximately 61.052 cm.