jmc

The area of the square is $s^2$. Since the sides of the square all have the same length, the base of the triangle is $s$ (for the height drawn). Therefore, the area of the triangle is $\frac{1}{2}sh$. Since these areas are equal, we have $$\frac{1}{2}sh=s^2.$$ Dividing both sides by $s$ and multiplying both sides by 2 gives $h=\boxed{2s}$.