Question 13
Let $d$ be the sum of the lengths of all diagonals of a flat convex polygon of $n$ vertexes $(n\gt 3)$, and let $p$ its perimeter. Demonstrate that $$
n-3\lt \frac{2d}{p}\lt \left[\frac{n}{2}\right]\left[\frac{n+1}{2}\right]-2
$$ being $[x]$ the whole part of $x$.
n-3\lt \frac{2d}{p}\lt \left[\frac{n}{2}\right]\left[\frac{n+1}{2}\right]-2
$$ being $[x]$ the whole part of $x$.