Answer
$x = 4\sqrt 3$
Work Step by Step
The geometric mean of two numbers is given by the following formula:
$\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are positive numbers and $x$ is the geometric mean.
Let's plug in our numbers:
$\frac{4}{x} = \frac{x}{12}$
Use the cross products property to get rid of the fractions:
$x^2 = 48$
Rewrite $48$ as the product of a perfect square and another factor:
$x^2 = 16 • 3$
Take the positive square root of each factor to solve for $x$:
$x = 4\sqrt 3$
