The perimeter of the triangle is 18 cm. Find the perimeter of the triangle, the vertices of which

The perimeter of the triangle is 18 cm. Find the perimeter of the triangle, the vertices of which are the midpoints of the sides of this triangle.

Let’s construct the vertices of the new triangle on the sides of the triangle ABC.

On the sides AB AC BC we construct points D, E, H, respectively.

Let’s construct a triangle DEH through these vertices.

The sides of triangle DEH are the midlines of triangle ABC.

The middle lines are half the parallel side.

DH = AC: 2;

DE = BC: 2;

EH = AB: 2.

The DEH sides are half the size of the ABC sides, so the perimeter is also half the size.

P = 18: 2 = 9.

Answer: 9.