Question 25
An equilateral triangle $\triangle \Delta$ of side length $L \gt 0$ is given. Suppose that $n$ equilateral triangles with side length $1$ and with non-overlapping interiors are drawn inside $\triangle \Delta$, such that each unit equilateral triangle has sides parallel to $\triangle \Delta$, but with opposite orientation. (An example with $n = 2$ is drawn below.)
Prove that
$$
n \le \frac{2}{3}L^2.
$$
Prove that
$$
n \le \frac{2}{3}L^2.
$$