# 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?

September 30, 2021 | education

| 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.

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