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.
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