Question

Один угол ромба составляет 120 °, длина диагонали этого угла составляет 10 см. Найдите периметр ритма

Answer 1

У ромба по две углы равны ,противоположенные например: 1угол 120 и протевоположенный угол 120
360-(120+120)=120
120/2=60.
А периметр равен 20

Answer 2

Получилось 2 треугольника причем равносторонних а значит периметр ромба равен 10*4=40

Answer 3

Finding the Perimeter of a Rhombus

To find the perimeter of a rhombus, we need to know the length of its side. However, the given information in the question is about the angle and the diagonal of the rhombus, not the side length. Therefore, we need to use some geometric properties of a rhombus to find the missing information.

A rhombus is a quadrilateral with all four sides of equal length. It also has some unique properties, such as opposite angles being equal and diagonals bisecting each other at right angles.

Let's use the given information to find the missing side length and then calculate the perimeter of the rhombus.

Finding the Side Length of the Rhombus

We are given that one angle of the rhombus measures 120° and the length of the diagonal is 10 cm. To find the side length, we can use the properties of a rhombus.

In a rhombus, the diagonals bisect each other at right angles. This means that the diagonal divides the rhombus into four congruent right-angled triangles.

Let's consider one of these triangles. The given angle is 120°, and we know that the diagonal divides the triangle into two equal sides. Let's call the side length of the rhombus "s".

Using trigonometry, we can find the length of one of the equal sides of the triangle. The sine of an angle is equal to the ratio of the length of the opposite side to the hypotenuse. In this case, the opposite side is half of the side length "s/2", and the hypotenuse is the given diagonal length of 10 cm.

So, we have:

sin(120°) = (s/2) / 10

Solving for "s", we get:

s/2 = 10 * sin(120°) s/2 = 10 * (√3/2) s/2 = 5√3 s = 10√3

Therefore, the side length of the rhombus is 10√3 cm.

Calculating the Perimeter of the Rhombus

Now that we know the side length of the rhombus, we can calculate its perimeter. The perimeter of any polygon is the sum of the lengths of its sides.

Since a rhombus has four equal sides, the perimeter of the rhombus is:

Perimeter = 4 * side length

Substituting the value of the side length we found earlier, we get:

Perimeter = 4 * 10√3 cm Perimeter = 40√3 cm

Therefore, the perimeter of the rhombus is 40√3 cm.

Please note that the calculations provided are based on the given information and assumptions about the properties of a rhombus.