Question

In triangle PQR, PS is median. Show that PQ + QR + RP > 2PS.

Answer 1

$\textbf{\huge{\underline{ Hello Mate! }}}$

$\textsf{\green{Given}}$ : PS is median in triangle PQR

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

$\textsf{\green{Proof}}$ : 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

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

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

$\textbf{ Have great future ahead! }$