Right Triangle Challenge: Find Side Length Given Area 10.5 and Height 3

A right triangle is shown below.

Its area is 10.5.

Calculate the length of side BC.

To solve for the length of side $BC$ in the right triangle, we will use the area formula for triangles:

• Step 1: Identify the given elements: $\text{Area} = 10.5$ and one leg $AB = 3$.
• Step 2: Use the formula for the area of a right triangle:
  $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
• Step 3: Substitute the known values into the formula:
  $10.5 = \frac{1}{2} \times 3 \times BC$
• Step 4: Solve for $BC$:
  Multiply both sides by 2 to clear the fraction:
  $21 = 3 \times BC$
• Step 5: Divide both sides by 3 to isolate $BC$:
  $BC = \frac{21}{3} = 7$

Therefore, the length of side $BC$ is $\boxed{7}$.