In triangle ABD, AB is 3 cm long and BD is 5 cm long. According to the triangle inequality theorem, which two lengths are possible lengths of AD?
Options:
10 cm
7 cm
4 cm
1 cm
2 cm
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 that AB is 3 cm and BD is 5 cm, the possible lengths for AD can be calculated using the triangle inequality theorem as follows:
1. AD + AB > BD
AD + 3 > 5
AD > 5 - 3
AD > 2 cm
2. AD + BD > AB
AD + 5 > 3
AD > 3 - 5
AD > -2 cm
Since the length of a side cannot be negative, the only possible lengths for AD are 2 cm and 10 cm.
Therefore, the correct options are:
- 10 cm
- 2 cm