Question

find the value of x.
x =

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
In the given right - triangle, the segment with length \(4x\) is the mid - segment and the side parallel to it has length \(48\).
So, we have the equation \(4x=\frac{48}{2}\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \(\frac{48}{2}=24\).
The equation becomes \(4x = 24\).
Divide both sides of the equation by \(4\): \(x=\frac{24}{4}\).
Since \(\frac{24}{4}=6\), we get \(x = 6\).

Answer:

\(x = 6\)