Right Triangle Area Problem: Find BC When Area = 38 cm² and AC = 8 cm

To solve this problem, we'll follow these steps:

• Step 1: Identify the area formula related to a right triangle.
• Step 2: Set up an equation with the given area and known side.
• Step 3: Solve for the unknown side $BC$.

Step 1: We know the area $A$ of a right triangle is given by the formula:
$A = \frac{1}{2} \times \text{base} \times \text{height}$.

Step 2: Using the known values, $A = 38 \, \text{cm}^2$, the side $\text{AC} = 8 \, \text{cm}$ and assuming it acts as the base, we set up the equation:
$38 = \frac{1}{2} \times 8 \times \text{BC}$.

Step 3: Simplify to solve for $\text{BC}$:
Multiply both sides by 2 to eliminate the fraction:
$76 = 8 \times \text{BC}$.
Now, divide both sides by 8 to find $\text{BC}$:
$\text{BC} = \frac{76}{8}$.
$\text{BC} = 9.5 \, \text{cm}$.

Therefore, the length of side $BC$ is 9.5 cm.