Solution to Principle of Insufficient Reason Introductory Problem 1

Problem 1

$\text{Principle of Insufficient Reason} \implies \text{max} ([\text{hexagon}])=[\text{Regular Hexagon}]=\boxed{\frac{3}{2} \sqrt{3}}$

Principle of Insufficient Reason $\implies$ the max of $e$ is achieved when $a=b=c=d$ so $4a+e=8$ $4a^2+e^2=16$ $\implies e=\frac{16}{5}$