Right Triangle Side Length: Find BC When Area = 40 and Height = 10

ABC is a right triangle with an area of 40.

Calculate the length of side BC.

The problem provides the area of a right triangle $ABC$, which is 40, and tells us that $AB = 10$, one of the legs. We need to find the base $BC$ of the triangle.

To find $BC$, we use the formula for the area of a triangle:

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

Here, the area is 40, the height $AB$ is 10, and the base is $BC$:

$40 = \frac{1}{2} \times BC \times 10$

We can simplify this equation to solve for $BC$:

$40 = 5 \times BC$
$BC = \frac{40}{5}$
$BC = 8$

Hence, the length of side $BC$ is $\boxed{8}$.