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
?
wright an equation for this for 4cm and 7cm

Answer 1

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

For AD to be possible, the sum of AB and BD must be greater than AD:
AB + BD > AD
3 + 5 > AD
8 > AD

So, 8 cm is a possible length for AD.

For AD to be possible, the difference of AB and BD must be less than AD:
|AB - BD| < AD
|3 - 5| < AD
2 < AD

So, 2 cm is a possible length for AD.

Therefore, the possible lengths for AD in triangle ABD are 2 cm, 4 cm, 5 cm, 6 cm, 7 cm, and 8 cm.