Right Triangle Side Length: Find BC When Area = 32 and Height = 8

ABC is a right triangle with an area of 32.

Calculate the length of side BC.

To solve this problem, we need to calculate the length of side $BC$ in triangle $\triangle ABC$ given that the area is 32 and side $AB = 8$.

We start by using the area formula for a right triangle:

In this context, the base $AB$ is 8, and the height $BC$ is the unknown we need to find. Thus, we have:

We can simplify this equation:

Now, solve for $BC$ by dividing both sides of the equation by 4:

Therefore, the length of side $BC$ is $\mathbf{8}$.

Thus, the solution to the problem is $BC = 8$.