The height of the triangle is the distance from the vertex (2, −1) to the base \(x + y - 2 = 0\):

\(h = \frac{|2 - 1 - 2|}{\sqrt{2}} = \frac{1}{\sqrt{2}}\)

For an equilateral triangle, \(h = \frac{\sqrt{3}}{2}a\), so

\(a = \frac{2h}{\sqrt{3}} = \frac{2}{\sqrt{2}\sqrt{3}} = \sqrt{\frac{2}{3}}\)

Answer: (C) \(\sqrt{\frac{2}{3}}\)