Question

ABCD is a quadrilateral
Is AB+BC+CD+DA>2(AC+BD)? ​

Answer 1

ANSWER:-

Given:

ABCD is a quadrilateral.

To find:

AB + BC +CD + DA>2(AC+BD).

Proof:

In a ∆, sum of any sides is always greater than the third side.

In ∆AOB,

AO + BO> AB..........(1)

In ∆BOC,

BO + CO > BC..........(2)

In ∆COD,

CO + DO >CD...........(3)

In ∆DOA,

DO + AO> AD.............(4)

Adding equation (1),(2),(3)&(4) we get;

AO+BO+BO+CO+CO+DO+DO+AO>AB+BC+CD+AD

=2AO+2BO+2CO+2DO>AB+BC+CD+AD

=)2(AO + CO+BO +DO)>AB+BC+CD+AD

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

Or

AB+BC+CD+DA<2(AC + BD) [Proved]

Hope it helps ☺️

Answer 2

Answer:

Refer to the attachment above. ⬆️

hope it helps!!