Find the perimeter of the rhombus if one of the corners of the rhombus is 60

Find the perimeter of the rhombus if one of the corners of the rhombus is 60 *, and the diagonal opposite this corner is 11 cm.

Find the length of the side of this rhombus.

Let us denote it by x.

Consider an isosceles triangle, where the sides are two sides of the rhombus forming an angle of 60 °, and the base is the diagonal of the rhombus, equal to 11 cm.

Using the cosine theorem, we can write the following equation:

x ^ 2 + x ^ 2 – 2x ^ 2 * cos (60 °) = 11 ^ 2.

Solving this equation, we get:

2x ^ 2 – 2x ^ 2 * cos (60 °) = 121;

2x ^ 2 – 2x ^ 2 * (1/2) = 121;

2x ^ 2 – x ^ 2 = 121;

x ^ 2 = 121;

x ^ 2 = 11 ^ 2.

x = 11 cm.

Knowing the length of the side of the rhombus, we find its perimeter:

4 * 11 = 44 cm.

Answer: the perimeter of the rhombus is 44 cm.