Problem (Geometry):
Quadrilateral $A R M L$ is a kite with $A R=R M=5, A M=8$, and $R L=11$. Compute $A L$.

Solution:
Let $K$ be the midpoint of $\overline{A M}$. Then $A K=K M=8 / 2=4, R K=\sqrt{5^{2}-4^{2}}=3$, and $K L=11-3=8$. Thus $A L=\sqrt{A K^{2}+K L^{2}}=\sqrt{4^{2}+8^{2}}=4 \sqrt{5}$.

Final answer: $4 \sqrt{5}$