Right Triangle Side Length: Finding BC When Area = 21

ABC is a right triangle with an area of 21.

Calculate the length of side BC.

To solve the problem, we start by identifying that the area of a right triangle is given by the formula:

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

Given: $\text{Area} = 21$ and one leg of the triangle, say the height $AB = 7$.

We denote the other leg, which we need to find, as $BC$. Thus:

$21 = \frac{1}{2} \times 7 \times BC$

Solving for $BC$, first multiply both sides by 2 to isolate the product of $7$ and $BC$:

$42 = 7 \times BC$

Now, divide both sides by 7 to solve for $BC$:

$BC = \frac{42}{7} = 6$

Therefore, the length of side $BC$ is $\mathbf{6}$.