Find the Cuboid Length: Solving Volume = 12X with Height 4cm

To solve this problem, we follow these steps:

• Step 1: Use the cuboid volume formula $\text{Volume} = \text{length} \times \text{width} \times \text{height}$.
• Step 2: Substitute the expressions for length $(X + 2)$, width $X$, and height $4$ into the formula.
• Step 3: Equate the expression to the given volume $12X$ and solve for $X$.
• Step 4: Once $X$ is determined, calculate the length as $X + 2$.

Now, let's work through each step:

Step 1: The formula for volume is:

$\text{Volume} = \text{length} \times \text{width} \times \text{height}$

Step 2: Substitute the given values:

$\text{Volume} = (X + 2) \times X \times 4 = 12X$

Step 3: Solve for $X$:

Expanding the left side, we have:

$(X^2 + 2X) \times 4 = 12X$

This simplifies to:

$4X^2 + 8X = 12X$

Rearranging gives:

$4X^2 + 8X - 12X = 0$

$4X^2 - 4X = 0$

Factor out $4X$:

$4X(X - 1) = 0$

Thus, $4X = 0$ or $X - 1 = 0$. The only meaningful solution (since $X$ can't be zero) is:

$X = 1$

Step 4: Calculate the length:

The length is $X + 2 = 1 + 2 = 3$ cm.

Therefore, the length of the cuboid is $3 \text{ cm}$.