In the ABC triangle, the height BD, which length is 12 cm, divides the AC side into segments AD = 5 cm and DC = 16 cm, find the perimeter of the triangle.
1. In triangle ABD, side AB is a leg, the length of which is calculated by the formula:
AB = √AD ^ 2 + BD ^ 2 = √5 ^ 2 + 12 ^ 2 = √169 = 13 cm.
2. In the BCD triangle, the BC side is the leg, the length of which is calculated by the formula:
ВС = √СD ^ 2 + ВD ^ 2 = √16 ^ 2 + 12 ^ 2 = √400 = 20 cm.
3. АС = АD + СD = 5 + 16 = 21 cm.
4. Calculate the total length of all sides of the triangle (perimeter):
AB + BC + AC = 13 + 20 + 21 = 54 cm.
Answer: the total length of all sides of the triangle (perimeter) is 54 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.