Question

5. In a quadrilateral OPQR , show that
( ii ) sum of its sides < 2 ( sum of its diagonals )​

Answer 1

Answer:

Step-by-step explanation:

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

AB+BC+CD+DA>AC+BD

Step-by-step explanation:

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