Question

Why do we use a platinum iridium alloy in making prototype meters and kilograms?

Answer 1

Recall that the prototype meter and kilogram are standardized bases that define the value of mass of a kilogram and length of a metre. This means that the prototype should not be easily influenced by change, both physically and chemically. Think of how this is established by the Pt-Ir alloy. In other words, Ir is added to platinum to reinforce it. Remember to think in terms of what physical and chemical properties does this reinforcement help with.

Complete answer:
Let us begin by first understanding what a prototype means in this context.
In order to define a unit for any physical quantity, there has to be a physical basis for its definition and the value it imbibes. This basis on which units are defined are called prototypes, and these prototypes are referred to as the international standards of measure for those units of physical quantities that are founded upon them. These prototypes are expected to be physically stable, dense, and resistant to oxidation in addition to many other properties that we will look at later.
Now, the question suggests that the prototype meter and the prototype kilogram are based on measures of platinum iridium (Pt-Ir) alloy. This means that the Pt-Ir alloy was used to define the mass of a kilogram and the length of a metre.
Note that the Pt-Ir alloy used in both cases were 90% platinum and 10% iridium by mass.
The international prototype of Kilogram (IPK) which is made up of Pt-Ir is a golf-ball sized circular cylinder with a height equal to its diameter. The 10% Iridium makes the alloy hard, while still retaining platinum’s many characteristics like extreme resistance to oxidation, extremely high density, low magnetic susceptibility. This ensures that the IPK does not gain or lose any mass and the mass of kilogram remains standard throughout.
The international prototype of metre(IPM) is also made up of Pt-Ir alloy bars that have an X-shaped cross section, also known as the Tresca cross-section to minimize effects of torsional strain during length comparisons. Pt-Ir alloy is stiffer and more resistant to chemicals and wear and tear than pure platinum. It also has a low thermal coefficient of expansion, which means that its structural fluctuations with changes in temperature is also low.
These are the reasons why the Pt-Ir alloys were used for defining the IPK and IPM.

Note:
The Pt-Ir alloy was used as the IPK and IPM until early 2019, but following some increasing divergence in the masses of the worlds prototypes and its short term instability, the IPK and IPM have their basis now set on values of some physical constants though the value of the kilogram and metre still remain the same.
The redefinition gives the units and their fundamental constants as:
Meter – Defined as the distance travelled by light in vacuum in $1/299,792,458$ seconds.
Kilogram - Defined as the Planck’s constant divided by $6.626 \times 10^{-34}\;m^{-2}s$
Thus, there is only a change in the basis of definition, but the result of the definition (value of the units) remains the same, i.e., a meter is still the measure of length and the kilogram is still the measure of mass.