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Problem 537

AMC 12 late, AIME early

Geometry Difficulty 4.9 Find the answer

5. [5] Joe has a triangle with area $\sqrt{3}$ . What's the smallest perimeter it could have?

Your answer

Official solution

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.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.