Right Triangle Side Length: Finding BC When Area = 10 and Height = 4

To find the length of side $BC$, follow these steps:

Step 1: Identify the given information

• The area of the triangle is given as $10$.
• The height $AB$ is $4$.

Step 2: Apply the area formula for a right triangle

The formula for the area $A$ of a triangle is:

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

Step 3: Set up the equation

Substituting the known values into the formula gives:

$10 = \frac{1}{2} \times BC \times 4$

Step 4: Solve for $BC$

Begin by simplifying the equation:

$10 = 2 \times BC$

Dividing both sides by 2 to solve for $BC$, we obtain:

$BC = \frac{10}{2} = 5$

Therefore, the length of side $BC$ is $5$.