One of the corners of the rhombus is 120 degrees, and the diagonal drawn from the vertex

| September 7, 2021 | education

One of the corners of the rhombus is 120 degrees, and the diagonal drawn from the vertex of the other corner is 8√3 Find the perimeter of the rhombus.

1. The vertices of the rhombus A, B, C, D. ∠B = 120 °. Diagonal AC = 8√3 units of measurement. О is the point of intersection of the diagonals.

2. Triangle AOB is rectangular, since, according to the properties of the rhombus, the diagonals intersect at right angles. That is, ∠AOB = 90 °.

3. According to the properties of the rhombus, each of its diagonals is the bisector of the angle from which it is drawn. That is, ∠ABO = 120: 2 = 60 °.

4. We calculate the length of the side AB of the triangle AOB through the sine ∠ABO:

AO / AB = sine ∠ABO.

Sine 60 ° = √3 / 2.

Since the diagonals are halved by the intersection point, AO = 8√3: 2 = 4√3 units.

AB = AO / √3 / 2 = 4√3 / √3 / 2 = 8 units.

5. Considering that all sides of the rhombus are equal, we calculate the perimeter (P) of this geometric figure:

P = 8 x 4 = 32 units.

Answer: the perimeter of a rhombus is 32 units.



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