Question

2. Периметр параллелограмма равен 60 см. Разность двух его углов равна 60°, а разность двух его сторон — 4 см. Найдите площадь параллелограмма. - пж памогите сор ​

Answer 1

Ответ:

х-одна сторона параллелограмма

у - другая сторона

{ 2(х+у)=60

х-у= 4; х=4+у

Подставим в первое уравнение:2(4+у+у)=60

4у+ 8=60; 4(у+2)=60; у+2=15; у=13

х=4+13=17

х=13; у=17

α- один угол

β- другой

{2(α+β)=360

α-β=60; α=60+β;

2(60+β+β)=360; 60+2β=180; 2β=180-60; 2β=120

β=60°, α=120°

S=xySin60°; S=17•13•Sin60°; S=221√3/2

Ответ: Площадь параллелограммаравна 221√3/2см²или приблизительно 191см²

Answer 2

Given Information:

We are given the following information about a parallelogram: - The perimeter of the parallelogram is 60 cm. - The difference between two of its angles is 60°. - The difference between two of its sides is 4 cm.

Solution:

To find the area of the parallelogram, we need to use the given information and apply relevant formulas.

Let's denote the length of one side of the parallelogram as a and the length of the adjacent side as b. The formula for the perimeter of a parallelogram is:

Perimeter = 2(a + b)

From the given information, we know that the perimeter is 60 cm. Therefore, we can write the equation:

60 = 2(a + b)

Simplifying the equation, we get:

a + b = 30 ---(Equation 1)

Next, let's consider the difference between two angles of the parallelogram. The opposite angles of a parallelogram are equal. Therefore, if we denote one angle as x, the other angle will be x + 60°. The sum of the angles of a parallelogram is 360°. So, we can write the equation:

x + (x + 60°) + x + (x + 60°) = 360°

Simplifying the equation, we get:

4x + 120° = 360°

Subtracting 120° from both sides, we get:

4x = 240°

Dividing both sides by 4, we get:

x = 60°

Therefore, one angle of the parallelogram is 60°.

Now, let's consider the difference between two sides of the parallelogram. We are given that the difference is 4 cm. Therefore, we can write the equation:

a - b = 4 ---(Equation 2)

We now have two equations (Equation 1 and Equation 2) with two variables (a and b). We can solve these equations simultaneously to find the values of a and b.

Solving Equation 1 and Equation 2 simultaneously, we get:

a = 17 and b = 13

Now that we have the values of a and b, we can calculate the area of the parallelogram using the formula:

Area = base × height

In a parallelogram, the base is one of the sides, and the height is the perpendicular distance between the base and the opposite side.

Since the opposite sides of a parallelogram are parallel, the height is the same as the length of the side perpendicular to the base. Therefore, the height of the parallelogram is b = 13 cm.

Using the formula for the area, we have:

Area = a × b = 17 cm × 13 cm = 221 cm²

Therefore, the area of the parallelogram is 221 cm².