By connecting the midpoints of the sides of the triangle, we get a triangle whose perimeter is 65.

By connecting the midpoints of the sides of the triangle, we get a triangle whose perimeter is 65. Find the perimeter of this triangle.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

The segment connecting the midpoints of its two sides is called the midline of the triangle. The middle line of the triangle is parallel to the third side, and its length is half the length of this side:

A1B1 = AB / 2;

B1C1 = BC / 2;

A1C1 = AC / 2.

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

P = AB + BC + AC;

P1 = A1B1 + B1C1 + A1C1.

Since all sides of the triangle ΔА1В1С1 are two times smaller than the sides of triangle ΔАВС, then the perimeter P1 of triangle ΔА1В1С1 is half the perimeter P of triangle ΔАВС. Thus:

P = P1 ∙ 2;

P = 65 ∙ 2 = 130 cm.

Answer: the perimeter of the triangle ΔABS is 130 cm.