Question 29
Sets $A$ of one hundred different natural numbers are considered, which have the property that if $a, b, c$ are any elements (equal or different) of $A$, there exists a non-obtuse triangle whose sides measure $a, b$ and $c$ units.
The sum of the perimeters considered in the definition of $A$ is called $S(A)$. Calculate the minimum value of $S(A)$.
The sum of the perimeters considered in the definition of $A$ is called $S(A)$. Calculate the minimum value of $S(A)$.