In triangle ABD, AB is 3cm long and BD is 5cm long. According to the triangle inequality theorem which two lengths are possible lengths of AD
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 triangle ABD, let AD be x cm long.
So, according to the triangle inequality theorem:
AB + BD > AD
3 + 5 > x
8 > x
Also,
AD + AB > BD
x + 3 > 5
x > 2
Therefore, the possible lengths of AD are between 2cm and 8cm.