Question

5. In a quadrilateral OPQR, show that :
(1) sum of its sides > sum of its diagonals, and
(i) sum of its sides < 2 (sum of its diagonals)​

Answer 1

Answer:

I oneof two diagonal is sum 2

Answer 2

Answer:

Consider a quadrilateral ABCD

Consider ΔACD

By triangle inequality

AC<AD+CD⋯(1)

Consider ΔACB

By triangle inequality

AC<AB+CB⋯(2)

Consider ΔBCD

By triangle inequality

BD<BC+CD⋯(3)

Consider ΔADB

By triangle inequality

BD<AD+AB⋯(4)

Adding all the equations

2(AB+BC+CD+AD)>2(AC+BD)

AB+BC+CD+DA>AC+BD