Question

34. In a quadrilateral ABCD.prove that AB + BC + CD +AD>AC+BD.​

Answer 1

Answer:

Given:ABCD is a quadrilateral whose diagonals AC and BD.

RTP:AB+BC+CD+AD>AC+BD

Proof:In triangle ABC,

AB+BC>AC.....(1)

In triangle BCD,

BC+CD>BD.....(2)

In triangle ACD,

AD+CD>AC.....(3)

In triangle ADB,

AD+AB>BD.....(4)

Adding 1,2,3,4

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

=AB+BC+CD+AD>AC+BD

Hence,proved.