Kilogram, is the basic unit of mass in the International System of Units ( SI) , and your employer is defined as the mass of the international prototype is composed of an alloy of platinum and iridium, my question is, why these and not others metals like gold or silver ?
The Wikipedia article on the kilogram at least touches on the reasons to use Pt-Ir. I can touch on several of the main ones.
You don't want the standard sitting around and oxidizing (which would add mass to the standard). So, gold would be good, silver definitely not (it oxidizes readily). Platinum is as good as gold (pun intended) when it comes to oxidation resistance.
You need to be able to handle the artifact without losing any mass. So, it needs to be quite hard (in a mechanical sense). Gold is very soft - if you dropped the standard, you would likely 'smear' some gold on to the surface. Platinum (pure) is harder than gold (on the Mohs scale Au is 2.5 and Pt is 3.5). Alloying Platinum with Iridium (Moh hardness 6.5) of Osmium (Moh hardness 7.0) makes it even harder (Platinum-osmium is/was used for the ball of good ball-point pens - it has high hardness and excellent tribological properties). By contrast, gold can be hardened somewhat through alloying, but 'hard' gold will never be as hard as the platinum-iridium alloys.
So, the Pt-Ir (90/10) used is inert (mostly) and hard (harder than gold).
As another example, platinum alloys are great in spark plugs; gold would be a disaster. Very different conditions, but from an inertness and hardness point of view perhaps not all that different.