The base of a parallelogram is twice its height. If the area of the parallelogram is 338 cm², then find its height (in cm).

The correct answer is 13.

Step 1: Define the relationship between base and height
Let the height of the parallelogram be $h$ cm.
Given that the base is twice its height, the base $b$ can be expressed as:

$b=2h$

Step 2: Use the formula for the area of a parallelogram
The area of a parallelogram is given by:

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

Substitute the given area (338 cm²) and the expression for base into the formula:

$338=2h\times h$

$2h^2=338$

Step 3: Solve for height ($h$)
Divide both sides of the equation by 2:

$h^2=169$

Take the square root of both sides:

$h=\sqrt{169}$

$h=13\text{cm}$

Therefore, the height of the parallelogram is 13 cm.