2. [4] Let $A B C$ be a triangle, and let $M$ be the midpoint of side $A B$. If $A B$ is 17 units long and $C M$ is 8 units long, find the maximum possible value of the area of $A B C$.
Answer: 68 Let $h$ be the length of the altitude from $C$ to $A B$. Observe that $K=\frac{1}{2} \cdot h \cdot A B \leq$ $\frac{1}{2} \cdot C M \cdot A B=68$ and that equality is achieved when $C M \perp A B$.