Two sides of a triangle have lengths of 16 cm and 17 cm. Which could be the length of the third side?

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

x - third side

if x ≤ 16 < 17 or 16 ≤ x < 17 then

x + 16 > 17 |-16

x > 1

x ∈ (1; 16]

if 16 < 17 ≤ x then

16 + 17 > x

33 > x

x ∈ [17; 33)

Answer: x ∈ (1; 16] ∪ [17; 33) → 1 < x ≤ 16 or 17 ≤ x < 33