Question

ABCD is a quadrilateral, prove that AB+BC+CD+DA < 2(AC+BD)​

Answer 1

Answer:

Step-by-step explanation:

AC is Hypotenuse in triangle ABC.

so,

AB<AC---1

BC<AC---2

because hypotenuse is the biggest one in Right triangle.And ABCD is quardrilateral so ABC is Right triangle.

similarly,

DA<BD---3

CD<BD---4

Now from 1,2,3& 4

AB+BC+CD+DA<(AC+AC)+(BD+BD)

=>AB+BC+CD+DA<2(AC+BD)