The midsegment determines a smaller triangle that is similar to the larger triangle. If two triangles are similar, then their side lengths are at the same ratio, so that:
[tex]\begin{gathered} \frac{5x}{45}=\frac{20}{20+16} \\ \frac{5x}{45}=\frac{20}{36} \end{gathered}[/tex]
From this expression, you can determine the value of x:
-First. multiply both sides by 45:
[tex]\begin{gathered} 45(\frac{5x}{45})=45(\frac{20}{36}) \\ 5x=25 \end{gathered}[/tex]
-Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{5x}{5}=\frac{25}{5} \\ x=5 \end{gathered}[/tex]
The value of x is equal to 5
