Question

параллелограмм и прямоугольник имеют равные стороны .Площадь прямоугольника в два раза больше площади параллелограмм.найдите острый угол параллелограмма

Answer 1

пусть

а-длина

b-ширина прямоугольника

тогда его площадь равна аb

 

тогда а-длина основания параллелограмма:

b-длина боковой стороны параллелограмма

его площадь равна а*h,где h-высота параллелограмма

высота параллелограмма является противолежащим катетом

значит он равен b*sinα,где α-острый угол параллелограмма.Из условия

аb=2 а*h=2аb*sinα,

отсюда

sinα=аb/2аb=1/2

значит α=30°

Answer 2

Finding the Angle of the Parallelogram

To find the acute angle of the parallelogram, we can use the fact that a parallelogram's opposite angles are equal. Let's denote the acute angle of the parallelogram as x.

Given that the parallelogram and rectangle have equal sides, we can use this information to find the acute angle of the parallelogram.

The acute angle of the parallelogram can be found using the following formula: \[ \text{acute angle} = \arctan\left(\frac{\text{opposite side}}{\text{adjacent side}}\right) \]

Let's calculate the acute angle using the given information.

Calculation

Given: - The area of the rectangle is twice the area of the parallelogram. - The sides of the parallelogram and rectangle are equal.

Using the given information, we can calculate the acute angle of the parallelogram.

The formula for the area of a parallelogram is: \[ \text{Area} = \text{base} \times \text{height} \]

The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \]

Let's denote the sides of the parallelogram and rectangle as follows: - Parallelogram: base = b, height = h - Rectangle: length = l, width = w

Given that the area of the rectangle is twice the area of the parallelogram, we have: \[ l \times w = 2 \times b \times h \]

Since the sides of the parallelogram and rectangle are equal, we can also express the sides of the rectangle in terms of the base and height of the parallelogram: \[ l = b \] \[ w = h \]

Substituting these into the area equation, we get: \[ b \times h = 2 \times b \times h \]

Solving for the acute angle using the formula mentioned earlier, we can find the value of x.

Conclusion

By solving the equation and using the formula for the acute angle, we can find the exact value of the acute angle of the parallelogram.