Question

ABCD is quadrilateral. prove that (ab+bc+cd+da)>(ac+bd)

Answer 1

in triangle Dab .
ab+Da is greater than bd by inequality of tri. 1.
in triangle.bac
ab+bc is greater than ac 2.
on adding equation 1and2.
ad+ab+bc+ab is greater than nd+ac

Answer 2

in triangle acd, ad+dcis bigger than ac and in triangle abc ab+bc bigger than ac
therefore by adding both the equations
ad+dc+ab+bc is bigger than 2ac
similarly ad+dc+ab+bc is bigger than 2db
by adding both of them we get
2(ad+dc+ab+bc)is bigger than 2(ac+db)
then by cancelling both the 2s we get the answer