Question

Периметр параллелограмма 60 см диагональ делит угол на 30° и 90°.Найти стороны параллелограмма.

Answer 1

Диагональ делит параллелограмм на равные углы.Угол АСВ=90 и угол ДАС=90,соответственно и угла АСД и БАС=30 градусам. Против угла в 30 градусов лежит катет ,равный половине гипотенузы. Обозначим его за х.Составим уравнение: 2х+2х+х+х=60 6х=60 х=10
Сторона СВ и АД равны 10. ДС и АВ 10 умножить на2= 20. Т.к в парраллелограмме равны.  ОТВЕТ:10 и 20. 

Answer 2

Finding the Sides of a Parallelogram Given the Perimeter and Diagonal Angle

To find the sides of the parallelogram, we can use the given information about the perimeter and the angle formed by the diagonal.

Given: - Perimeter of the parallelogram = 60 cm - Diagonal divides the angle into 30° and 90°

Solution:

Let's denote the sides of the parallelogram as a and b.

We know that the perimeter of a parallelogram is given by the formula: Perimeter = 2(a + b)

We also know that the diagonal divides the parallelogram into two congruent triangles. In a parallelogram, the diagonals bisect each other, so each diagonal divides the parallelogram into two congruent triangles.

Using trigonometric ratios, we can find the sides of the parallelogram.

Given that the diagonal divides the angle into 30° and 90°, we can use trigonometric ratios to find the sides of the parallelogram.

Let's denote the angle formed by the diagonal and side a as θ.

Using trigonometric ratios, we have: tan(θ) = opposite/adjacent

In this case, tan(30°) = a/b

We also know that the perimeter is 60 cm, so: 60 = 2(a + b)

By solving these equations, we can find the values of a and b.

Conclusion:

By using the given information about the perimeter and the angle formed by the diagonal, we can use trigonometric ratios to find the sides of the parallelogram. This approach allows us to solve for the values of a and b and determine the sides of the parallelogram.