Let $G$ be a graph on $n$ vertices. Prove that if $|E| \ge 2kn$ then $G$ Contains a path of at least length $k$
I know the relationship between the number of edges and the sum of degrees Of the vertices. I also know that every graph contains a path at least the length of the minimum degree of $G$
I tried just using those relationships and coming to a conclusion, but I am stuck. I got to a point where i could show that $k \le n^2$ but wasnt sure if that helped me