Given an equilateral triangle ABC. The distance from the axis of symmetry to, passing through vertex B

Given an equilateral triangle ABC. The distance from the axis of symmetry to, passing through vertex B, to vertex A is equal to 3 cm. Find the perimeter of an equilateral triangle.

The axis of symmetry passing through the vertex B divides the ABC triangle into two right-angled triangles, where k is their common leg, which is 3 cm.

Let’s find the hypotenuse, which is the side of the triangle ABC:

sin A = k / AB;

sin A = 3 / AB.

Since the angle A = 60 °, we rewrite the formula:

3 / AB = sin 60 °;

3 / AB = 1/2 * √3;

AB = 6 * √3;

We find the perimeter of the triangle ABC, since all sides are equal, then we calculate this value:

3 * 6 * √3 = 18 * √3.

Answer: the perimeter of the ABC triangle is 18 * √3 cm.