Dissecting Triangles

The Triangle Midsegment Theorem tells us that, if a segment joins the midpoints of two sides of a triangle, then the segment is half as long as the third side.

We are told that $\overline{DE}$ is a midsegment of $△QST.$ Therefore, by the previous theorem, we can write an equation connecting $DE$ and $ST.$ $$\begin{array}{c}DE=\frac{1}{2}ST\end{array}$$ Now, we can find the value of $x$ by substituting the given values into this equation.