In the ABC triangle, the height BD, which length is 12 cm, divides the AC

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.