5. [5] Joe has a triangle with area $\sqrt{3}$. What's the smallest perimeter it could have?
Answer: 6 The minimum occurs for an equilateral triangle. The area of an equilateral triangle with side-length $s$ is $\frac{\sqrt{3}}{4} s^{2}$, so if the area is $\sqrt{3}$ then $s=\sqrt{\sqrt{3} \frac{4}{\sqrt{3}}}=2$. Multiplying by 3 to get the perimeter yields the answer.