Answer:
[tex]\large\boxed{2\sqrt7}[/tex]
Step-by-step explanation:
Look at the picture.
ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]
We have
[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]
Substitute:
[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex] cross multiply
[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]
