The perimeter of the triangle is equal to 18 cm. Find the perimeter of the triangle

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

The perimeter of a triangle is the sum of all its sides:

P = AB + BC + AC.

The segment connecting the midpoints of the two sides of the triangle is called the midline.

The middle line of the triangle is parallel to the third side, and its length is equal to half the length of this side.

Since the segment A1B1 is the middle of the sides AB and BC, it is parallel to the AC side, then:

A1B1 = AC / 2.

Since the segment B1C1 is the middle of the sides BC and AC, parallel to the side AB, then:

B1C1 = AB / 2.

Since the segment A1C1 is the middle of the sides AB and AC, parallel to the side BC, then:

A1C1 = BC / 2.

Since the length of the sides of the triangle A1B1C1 is equal to half the length of the sides of the triangle ABC, then the perimeter of PA1B1C1 is equal to half the perimeter of the triangle ABC:

PA1B1C1 = PABC / 2;

PA1B1C1 = 18/2 = 9 cm.

Answer: the perimeter of triangle A1B1C1 is 9 cm.