Question

In a quadrilateral abcd show that (AB +BC+CD+DA) >(AC +BD)

Answer 1

ABCD is a quad.Its diagonals are AC and BD.

In triangle ACB, AB + BC > AC - 1

In triangle BDC, BC + CD > BD - 2

In triangle ACD, AD + DC > AC -3

In triangle BAD, AB + AD > BD -4

Adding 1,2,3 and 4,

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

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

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

Answer 2

Hi..
See the attached file..

I hope it will help you