In triangle ABD

Question

, 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
?
Correct Answers
4 cm and 7 cm

Answer 1

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In triangle ABD, we have AB = 3 cm and BD = 5 cm.
To find possible lengths for AD, we need to consider the following inequalities:

AB + BD > AD
3 + 5 > AD
8 > AD

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

AD + BD > AB
AD + 5 > 3
AD > -2 (This inequality is not meaningful since lengths cannot be negative.)

Therefore, the possible lengths of AD are between 2 cm and 8 cm. The correct answers are 4 cm and 7 cm.