Is the following inequality holds true for all positive integers?

Question

If $a , b , c$ and $d$ are positive integers, and $ab$ is greater than $cd$, then, is $a+b$ greater than or equal to $c+d$, always true?

Answer 1

Not at all.

Consider $a=b=3$ and $c=1,d=8$. Then $ab=9$ while $cd=8$ however $a+b=6$ while $c+d=9$.

If you want a trivial example, you can take $c=0$, any non zero $a,b$. Then take $d$ very large.

Answer 2

Nope...consider: $$100=20 \times 5$$ and $$54=27 \times 2$$