Answer:
x = 8
Step-by-step explanation:
Look at the picture.
ΔABC and ΔACD are similar. Therefore corresponding sides are in proportion:
[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]
We have
[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]
Substitute:
[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=8[/tex]
