In triangle ABC, height BD divides side AC into segments AD and DC. It is known that AD = 5 cm

In triangle ABC, height BD divides side AC into segments AD and DC. It is known that AD = 5 cm, DC = 16 cm, BD = 12 cm.Find the perimeter of the triangle.

The height BD divides the triangle into two right-angled triangles, with a common leg of 12 centimeters and legs of 5 and 16 centimeters.

by the Pythagorean theorem, we calculate AB and BC:

AB = √12 ^ 2 + 5 ^ 2 = √144 + 25 = √169 = 13 centimeters.

BC = √16 ^ 2 + 12 ^ 2 = √256 + 144 = √400 = 20 centimeters.

Since the perimeter is the sum of all sides, then:

P = 13 + 20 + (5 + 16) = 33 + 21 = 54 centimeters.

Answer: The perimeter of triangle ABC is 54 centimeters.