in triangle abc ae , bd , cf are the medians show that ab+bc+ca 2(ae+bd+cf) - Maths - Triangles

Question

in triangle abc ae , bd , cf are the medians show that
ab+bc+ca>2(ae+bd+cf)

Lovina Kansal · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a0ef1a29b7e2%20png"
style="width: 357px; height: 291px;">
Correct question is In triangle ABC, AE,BD,CF are the medians
 Show that AB+BC+CA>AE+BD+CFWe know that the sum of any two sides of a triangle is greater thantwice the median bisecting the third side
Therefore,AE is the median bisecting BC⇒AB+AC>2AE    
(1)BD is the median bisecting AC⇒AB+BC>2BD    
(2)CF is the median bisecting AB⇒AC+BC>2CF     
(3)Adding (1),(2) and (3), we getAB+AC+AB+BC+AC+BC>2AE+2BD+2CF⇒2AB+BC+AC>2AE+BD+CF⇒AB+BC+AC>AE+BD+CF
Regards

in triangle abc ae , bd , cf are the medians show that ab+bc+ca>2(ae+bd+cf)