## Problem 11

The triangle $\mathrm{ABC}$ satisfies $0 \leq \mathrm{AB} \leq 1 \leq \mathrm{BC} \leq 2 \leq \mathrm{CA} \leq 3$. What is the maximum area it can have?


## Solution

If we ignore the restrictions of $\mathrm{CA}$, then the maximum area is 1 , achieved when $\mathrm{AB}$ is perpendicular to $\mathrm{BC}$. But in this case CA satisfies the restrictions.

