Finding the Ratio of Triangle Sides

In the coordinate plane, consider a right triangle where one vertex is at the origin (0, 0), another vertex is at the point (a, 0) on the x-axis, and the third vertex is at the point (0, b) on the y-axis. The area of the triangle is given by the formula:

$$ A = \frac{1}{2} \times \text{base} \times \text{height} $$

For this triangle, the base is $a$ and the height is $b$. Given that the area of the triangle is 24 square units, find the value of $\frac{b}{a}$.