Answer:
[tex]\large\boxed{x=3\sqrt5}[/tex]
Step-by-step explanation:
Look at the picture.
ΔABC and ΔDBA are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BD}{AB}[/tex]
We have
[tex]AB=x,\ BC=5+4=9,\ BD=5[/tex]
Substitute:
[tex]\dfrac{x}{9}=\dfrac{5}{x}[/tex] cross multiply
[tex]x^2=(9)(5)\to x=\sqrt{(9)(5)}\\\\x=\sqrt9\cdot\sqrt5\\\\x=3\sqrt5[/tex]
