Question

Question 9
AD is a median of the $\Delta ABC$. Is it true that AB + BC + CA > 2AD? Give reason for your answer.

Answer 1

Yes

In $\Delta ABD,\text{we have}AB+BD>AD....\left(i\right)$
[sum of any two sides of a triangle is greater than third side]
In $\Delta ACD$, we have AC +CD > AD ....(ii)
[sum of any two sides of a triangle is greater than third side]
on adding Eqs (i) and (ii) we get
(AB +BD +AC +CD) > 2 AD
$\Rightarrow (AB+BD+CD+AC)>2AD$
Hence, AB +BC +AC > 2 AD $[\because BC=BD+CD]$