Answer
F.
[tex]x=\sqrt{45}[/tex]
Step-by-step explanation
Triangles ABD and ACD are similar, then their corresponding sides are proportional, that is,
[tex]\frac{longest\text{ leg in ABD}}{longest\text{ leg in ABC}}=\frac{shortest\text{ leg in ABD}}{shortest\text{ leg in ABC}}[/tex]
From the diagram:
[tex]\frac{x}{9}=\frac{5}{x}[/tex]
Solving for x:
[tex]\begin{gathered} x\cdot x=5\operatorname{\cdot}9 \\ x^2=45 \\ \sqrt{x^2}=\sqrt{45} \\ x=\sqrt{45} \end{gathered}[/tex]
