Question

In ∆PQR , PS is the median. Prove that 2PS<(PQ+QR+RP).​

Answer 1

Answer:

iven : PS is median in triangle PQR

\textsf{\green{To prove}}To prove : PQ + QR + PR > 2PS.

\textsf{\green{Proof}}Proof : In triangle PQS

Sum of two sides is greater than the third side.

PQ + QS > PS ___(1)

In triangle PRS

Sum of two sides is greater than the third side.

PR + RS > PS ___(2)

Adding (1) and (2) we get

PQ + ( QS + RS ) + PR > PS + PS

\textsf{\blue{ PQ + QR + PR > 2PS }} PQ + QR + PR > 2PS

\textsf{\red{ Hence Proved ( Q.E.D ) }} Hence Proved ( Q.E.D )