Question

in a quadrilateral PQRS,PROVE THAT PQ+QR+RS+SP>PR+SQ

Answer 1

As shown the given image:
PQRS is quadrilateral, with diagonal PR and QS


Now,

QR+RS > QS -----(i)
PS+RS > PR -------(ii)
PS+PQ > QS ----(iii)
PQ+ QR > PR --------(iv)

By adding (i), (ii), (iii) and (iv)

2PQ + 2QR + 2RS + 2SP > 2PR + 2SQ

2(PQ+QR+RS+SP) > 2(PR + SQ)

Divide both sides by 2.
and TADA:

PQ+QR+RS+SP > PR +SQ