Question

In the figure, T is the mid point on the side QR of PQR and S is such a point such that TR=TS.
Prove that PQ+PR>QS

Answer 1

Since pqr is a triangle,pq+pr>qr(sum of smaller sides is always greater than largest side for a triangle to be possible).
Since tr=ts.
In triangle qst,qt+ts>qs
Ts>qs-qt
Pq+pr>qr
Pq+pr>tr+qt
Pq+qr>qs-qt+qt
Pq+qr>qs
Hence,Proved..