Question

Show that sum of all sides of quadrilaterals is greater than the sum of its diagonals

Answer 1

plzzz subscribe my youtube channel-
https://www.youtube.com/channel/UC27NLinpXVunbzVQ0vdHabQ

For any quadrilateral ABCD,ABCD, we can easily prove that

AB+BC+CD+DA>AC+BD......(1)(1)AB+BC+CD+DA>AC+BD......

Now, three cases arise. Either,

AC=BDorAC>BDorAC<BDAC=BDorAC>BDorAC<BD.

If AC=BDAC=BD,then the result follows from (1).

If AC>BD⟹AC+BD>2BDAC>BD⟹AC+BD>2BD and then the result follows from (1).

If BD>AC⟹AC+BD>2ACBD>AC⟹AC+BD>2AC and then the result follows from (1).

Answer 2

I think this is the brainliest answer