Question

Один из углов параллелограмма равен 45 градусов высота параллелограмма проведенная из вершины его тупого угла равна 4 сантиметра делит сторону параллелограмма на два данных отрезка периметр параллелограмма равен 27,4 найдите стороны параллелограмма, диогональ, проведенную из той же вершины что и высота

Answer 1

В паралелограмме если один угол равен 45 градусов то противоположый ему угол равен также 45 градусам. в паралелограмме сумма углов рана 360 градусов.из этого следует что сумма остальных углов =360-90(45+45)=270
Рассмотрим треугольник образовавшийся от вешрины.он равнобедренный так как углы при основании равны (90-45=45 45=45)если он равнобедренный то вершина рвна стороне от углав 45 градусов.сторона от угла равна 4 см так как высота разделила сторону пополам то тогда сторона от угла = 90 градусов до стороны = 270 градусов =4 см 4+4=8 противоположная сторона также равна 8 см 8+8=16
27,4-16=11,4 11,4/2=5,7- маленькая сторона так как это паралелограмм тогда противоположная сторона = также 5,7 см.
Ответ  8 см 8 см 5,7 см 5,7см

Answer 2

Given Information

We are given the following information about a parallelogram: - One of the angles of the parallelogram is 45 degrees. - The height of the parallelogram, drawn from the vertex of its obtuse angle, is 4 centimeters. - The height divides one of the sides of the parallelogram into two segments. - The perimeter of the parallelogram is 27.4.

Solution

To find the sides of the parallelogram, as well as the diagonal drawn from the same vertex as the height, we can use the given information and apply some geometric properties of parallelograms.

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

Finding the Sides of the Parallelogram

Since the height divides one of the sides of the parallelogram into two segments, we can consider the height as the sum of these two segments. Let's denote these segments as x and y.

According to the given information, the height of the parallelogram is 4 centimeters, and it divides one of the sides into two segments. Therefore, we have the equation:

x + y = 4 The perimeter of the parallelogram is given as 27.4. Since opposite sides of a parallelogram are equal in length, we can express the perimeter in terms of the sides:

2(a + b) = 27.4

Simplifying the equation, we have:

a + b = 13.7 Now we have a system of two equations with two variables:

x + y = 4 a + b = 13.7 We can solve this system of equations to find the values of x, y, a, and b.

Finding the Diagonal of the Parallelogram

To find the diagonal of the parallelogram, we can use the Pythagorean theorem. In a parallelogram, the diagonal, height, and one side form a right triangle.

Let's consider the right triangle formed by the diagonal, height, and one side. We can denote the diagonal as d and the side as a.

Using the Pythagorean theorem, we have:

d^2 = a^2 + 4^2

Simplifying the equation, we have:

d^2 = a^2 + 16

Now we have an equation to find the value of the diagonal d.

Solving the Equations

To solve the system of equations and find the values of x, y, a, b, and d, we can use substitution or elimination methods.

Using the substitution method, we can solve the first equation for x and substitute it into the second equation:

x = 4 - y

Substituting this value into the second equation, we have:

(4 - y) + y = 13.7

Simplifying the equation, we have:

4 + y = 13.7

y = 13.7 - 4

y = 9.7

Substituting the value of y back into the first equation, we have:

x + 9.7 = 4

x = 4 - 9.7

x = -5.7

Since the length of a side cannot be negative, we discard the negative value of x.

Therefore, we have:

x = 0

Now we can substitute the values of x and y into the equation for the diagonal:

d^2 = a^2 + 16

d^2 = (13.7 - b)^2 + 16

Simplifying the equation, we have:

d^2 = 187.69 - 27.4b + b^2 + 16

d^2 = b^2 - 27.4b + 203.69

Now we have an equation to find the value of the diagonal d.

To find the values of a, b, and d, we need additional information or equations. The given information does not provide enough information to uniquely determine the values of a, b, and d.

Please provide additional information or equations to solve for the sides of the parallelogram and the diagonal drawn from the same vertex as the height.