Let's begin with recalling the Geometric Mean Altitude Theorem.
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.
x/h=h/y or h=sqrt(x*y)Now, let's take a look at the given picture.
Using the theorem we recalled at the beginning, we can write a proportion.
8/x=x/4
We can solve for x using cross multiplication.
Our next step will be to take a square root of both sides of the equation. Notice that, since x represents a dimension, we will consider only positive case when taking a square root of x^2.
