The perimeter of a triangle formed by the middle lines of another triangle is 9 cm, then the perimeter of this triangle is …

1. A, B, C – the vertices of the triangle. DEF is a triangle formed by the middle lines.

DE, EF, DF – middle lines.

2. The middle line of a triangle is equal to half of the side parallel to it. Consequently,

AC = 2DE, AB = 2EF, BC = 2DF.

3. The perimeter of the triangle DEF = DE + EF + DF = 9 centimeters.

4. The perimeter of the triangle ABC = AB + BC + AC.

5. We replace in the last expression AC with 2DE, AB with 2ЕF, ВС with 2ДF.

The perimeter of the triangle ABC = 2DE + 2ЕF + 2DF = 2 (DE + ЕF + DF) = 2 x 9 = 18 centimeters.

6. The perimeter of triangle ABC is 18 centimeters.