Right Triangle Solution: Finding Side Length BC with Area 36

To solve for the length of side $BC$ in the right triangle $\triangle ABC$, we start with the formula for the area of a right triangle:

$\text{Area} = \frac{1}{2} \times AB \times BC$

We know the area of the triangle is 36, and the length of side $AB$ is 12. We'll substitute these values into the formula:

$36 = \frac{1}{2} \times 12 \times BC$

To isolate $BC$, first multiply both sides of the equation by 2 to eliminate the fraction:

$72 = 12 \times BC$

Now, solve for $BC$ by dividing both sides of the equation by 12:

$BC = \frac{72}{12}$

Upon simplifying, we find:

$BC = 6$

Thus, the length of side $BC$ is $\boxed{6}$.