# In triangle ABC, point K belongs to side AB, and point P to side AC. Segment КР || BC.

In triangle ABC, point K belongs to side AB, and point P to side AC. Segment КР || BC. Find the perimeter of the triangle AKP if AB = 16 cm, BC = 8 cm, AC = 15 cm and AK = 4 cm

A straight line parallel to the side of the triangle cuts off a triangle like this one from it. KR // BC according to the condition of the problem. Hence, we are considering similar triangles.

k = ВС / КР – coefficient of similarity, equal to the ratio of similar sides of similar triangles.

k = 8/4 = 2.

Now let’s remember one more property of such triangles. The ratio of the perimeters of similar triangles is equal to the coefficient of similarity. RABC / PAKP = k

Find the perimeter of the triangle ABC.

16 + 8 + 15 = 39 cm.

Perimeter of triangle AKP:

39: 2 = 19.5 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.