# In an equilateral triangle with a side of 8 cm, another triangle is inscribed with the vertices of which

In an equilateral triangle with a side of 8 cm, another triangle is inscribed with the vertices of which are the midpoints of the sides of the first; in the second triangle, a triangle is inscribed in the same way, and so on. Find the perimeter of the eighth triangle.

1) Consider first the first triangle after the main one. Each side of it is equal to half the side of the main triangle, and the perimeter is half the perimeter of the original triangle.

Let side a1 = 8 cm, perimeter p = 3 * a1 = 3 * 8 cm = 24 cm.

2) The next perimeter p2 = 3 * a2 = p1 / 2 = 24/2 = 12 cm. Next, we calculate the perimeter values, denoting the number of the triangle, we get:

3) p3 = p2 / 2 = 12 cm / 2 = 6 cm.

4) p4 = p3 / 2 = 6 cm / 2 = 3 cm.

5) p5 = p4 / 2 = 3/2 = 1.5 cm. 6) p8 = p1 / 2 ^ 8 = 24 cm / 256. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.