Answer
$b = \sqrt3a$
Work Step by Step
We set the equations for the area of a triangle and the area of an equilateral triangle equal to each other:
$\frac{\sqrt{3}}{4}s^2 = (1/2)(b)(h) \\\frac{\sqrt{3}}{4}(2a)^2 = (1/2)(2a)(b) \\ \sqrt{3}a^2 = ab \\ b = \sqrt3a$$
