Question 33
Points $A$, $B$ and $C$ are chosen in a rectangle of shape $7 \times 10$ in such a way that the distances from $A$ to some three sides of the rectangle are $2$, $3$ and $4$, the distances from $B$ to some three sides of the rectangle are $3$, $4$ and $5$, and the distances from $C$ to some three sides of the rectangle are $4$, $5$ and $6$. Find the largest possible area the triangle $ABC$ can have.