In a triangle, the sides are 11 cm, 12 cm, 13 cm, and its vertices are the midpoints of the sides of this triangle.

| April 26, 2021 | education

In a triangle, the sides are 11 cm, 12 cm, 13 cm, and its vertices are the midpoints of the sides of this triangle. Find the perimeter of the larger triangle.

A triangle is a figure that consists of three points that do not lie on one straight line, connected by segments.

Since the vertices of the ABC triangle are the stredins of the sides of the НKM triangle, the segments that connect these vertices are the midlines of the НKM triangle.

The middle line of a triangle is half the length of the side that is parallel to it:

AB = НM / 2;

BC = НK / 2;

AC = KM / 2.

In this way:

НM = 2AB;

НM = 11 * 2 = 22 cm;

НC = 2BC;

НK = 12 * 2 = 24 cm;

KM = 2AC;

KM = 13 * 2 = 26 cm.

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

P = НM + НK + KM;

P = 22 + 24 + 26 = 72 cm.

Answer: The perimeter of the larger triangle is 72 cm.



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.