Question

In triangle ABD, AB is 3 cm long and BD is 5 cm long. According to the Triangle Inequality Theorum, which two lengths are possible lengths of AD?

A. 4 cm
B. 2 cm
C. 7 cm
D. 10 cm
E. 1 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, AB = 3 cm, BD = 5 cm. Let's find the possible lengths of AD:

1. AD + AB > BD
AD + 3 > 5
AD > 2

2. AD + BD > AB
AD + 5 > 3
AD > -2 (Since AD cannot be negative, ignore this inequality)

Therefore, the possible lengths of AD are 2 cm and greater.

So, the two possible lengths of AD are:
A. 4 cm
C. 7 cm