Question

PS is a median of triangle PQR. Show that (PQ +PR)is greater than 2 PS

Answer 1

in ∆PQS
PQ+QS>PS ......(i)
Similarly in ∆PRS
RP+RS>PS .....(ii)

Now adding (i) and (ii) we get,
(PQ+QS)+(RP+RS)>PS+PS
PQ+(QS+RS)+RP>2PS
PQ+QR+RP>2PS