Question

In the following figure, S is any point on side BC of ΔABCΔABC. Then AB + BC + CA < 2AS

• A. True
• B. False

Answer 1

The correct option is B False

Consider $△ABS$

$AB+BS>AS$ ..... $\left(i\right)$

From $△ACS$

$AC+CS>AS$ .... $\left(ii\right)$

Adding $\left(i\right)$ and $\left(ii\right)$

$AB+BS+AC+CS>AS+AS$

$\therefore AB+BC+CA>2AS$

Hence, the statement is false.