Triangle Area Problem: Find Height X When Area = 12 and Base = 3

To solve this problem, we'll use the formula for the area of a triangle:

• Step 1: Identify the given information: Area = 12, base $BC = 3$, height $AE = x$.
• Step 2: Use the area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 3: Solve for $x$ (height) using $x = \frac{2 \times \text{Area}}{\text{base}}$.

Now, substituting the known values into the equation, we get:

$x = \frac{2 \times 12}{3}$

Performing the multiplication and division yields:

$x = \frac{24}{3} = 8$

Therefore, the length of $x$ is 8.