Discussion

The area of an equilateral triangle is \(\sqrt{3}\). What is the perimeter of the triangle?

Answer: C

The perimeter is 6.

An equilateral triangle of side \(a\) has area \(\frac{\sqrt{3}}{4}a^{2}\). Setting this equal to \(\sqrt{3}\):

\[ \begin{aligned} \frac{\sqrt{3}}{4}a^{2} &= \sqrt{3} \\ a^{2} &= 4, \quad a = 2 \end{aligned} \]

The perimeter is \(3a = 6\). 2 is the side itself, 4 is \(a^{2}\) or two sides, and 8 does not follow from the area.

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