Solve for X: Parallelogram Area 392 cm² with 2X and 4X Expressions

To find $X$, we use the formula for the area of a parallelogram:

$\text{Area} = \text{base} \times \text{height}$

Given that the area is 392 cm$^2$, and assuming $2X$ is the base and $4X$ is the height, we substitute these values into the formula:

$392 = (2X) \times (4X)$

Simplifying the right side gives us:

$392 = 2 \cdot 4 \cdot X^2 = 8X^2$

To solve for $X^2$, divide both sides by 8:

$X^2 = \frac{392}{8}$

$X^2 = 49$

Taking the square root of both sides, we find:

$X = \sqrt{49}$

$X = 7$

Therefore, the solution to the problem is $X = 7$ cm.