Final answer:
The third side of a triangle with other sides measuring 4 cm and 1.5 cm cannot be less than 2.5 cm or greater than 5.5 cm due to the triangle inequality theorem.
Step-by-step explanation:
The question pertains to the possible lengths of the third side of a triangle when the other two sides are given. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given two sides of a triangle are 4 cm and 1.5 cm, the length of the third side must be less than their sum (4 cm + 1.5 cm = 5.5 cm) and greater than their difference (4 cm - 1.5 cm = 2.5 cm). So, the third side cannot be less than 2.5 cm or greater than 5.5 cm.