# In triangle ABC it is known that AC = 16 cm, BC = 12 cm. Which of the given values can be equal to the length AB?

To solve, we apply the condition for the existence of a triangle.

The sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

Let’s check this condition for each case.

A).

AC = 16 cm, BC = 12 cm, AB = 4 cm.

BC + AB = 12 + 4 = 16 cm.

AC = (BC + AB) – the condition is not met.

B).

AC = 16 cm, BC = 12 cm, AB = 12 cm.

BC + AB = 12 + 12 = 24 cm.

AC + BC = 16 + 12 = 28 cm.

AC + AB = 16 + 12 = 28 cm.

The condition is met.

V).

AC = 16 cm, BC = 12 cm, AB = 28 cm.

AC + BC = 16 + 12 = 28 cm.

AB = (AC + BC) – the condition is not met.

G).

AC = 16 cm, BC = 12 cm, AB = 30 cm.

AC + BC = 16 + 12 = 28 cm.

(AC + BC) <AB – the condition is not met.

Answer: B) side AB can be 12 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.