Two sides of a triangle, the angle between which is 60 to refer to 5: 8, 3 sides is 21 cm find the perimeter

Let the length of the side BC = 5 * X cm, then, by condition, the length of the side AB = 8 * X cm.

Knowing the length of the AC side and the opposite angle, we use the cosine theorem for a triangle.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * CosABC.

441 = 64 * X ^ 2 + 25 * X ^ 2 – 80 * X * (1/2).

89 * X ^ 2 – 40 * X ^ 2 – 441 = 0.

49 * X ^ 2 = 441.

X ^ 2 = 441/49.

X = 21/7 = 3.

Then AB = 8 * 3 = 24 cm.

BC = 5 * 3 = 15 cm.

The perimeter of the ABC triangle will be equal to: Ravs = 15 + 24 + 21 = 60 cm.

Answer: The perimeter of the triangle is 60 cm.