Question

A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third​ side?

Answer 1

• The third side must be between 10cm and 14 cm

Explanation:

Let the third side be x

Triangle inequality theorem: sum of the length of any two sides must be greater than the third side length:

• 2 + 12 > x ⇒ x < 14
• 2 + x > 12 ⇒ x > 10
• x + 12 > 2 ⇒ x > -10, we change it to x > 0 as it should be a positive number

Combined together we have:

• 10 < x < 14

The third side must be between 10cm and 14 cm