Let $s$ be the scale factor of dilation. Then the ratio of the areas of the dilated triangle to the original triangle is $s^2$. We want this ratio to be 6.25, so $s^2 = 6.25 = \left( \frac{5}{2} \right)^2$. Since $s > 0$, we have $s = \boxed{\frac{5}{2}}$.
