Q: a: if two sides of a triangle are 3 cm and 5 cm in length, which could not be the measure of the third side? a) 2 cm b) 3 cm c) 4 cm d) 5 cm

A) 2cm

Step-by-step explanation:

According to the Triangle Inequality Theorem, the sum of the measure of any two sides of a triangle MUST be larger than the measure of the third side.  In this case, with sides 3cm and 5cm, the third side would have to be at least 3cm in order for the smallest two sides to be larger than the third side:

3cm + 3cm = 6 cm > 5cm

However, if the third side was only 2cm, then the two smaller sides would be 5cm, which is only equal to and not larger than the third side:

3cm + 2cm = 5cm

Any other measurements larger than 3cm, when added to the given side of 3cm, would be larger than 5cm and would form a triangle.  So, the only measure that would NOT form a triangle would be 2cm.

step-by-step explanation: