Answer:
[tex]\large\boxed{x=15}[/tex]
Step-by-step explanation:
ΔABC and ΔDB are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BD}{AB}[/tex]
We have
AB = x
BC = 25
BD = 9
Substitute:
[tex]\dfrac{x}{25}=\dfrac{9}{x}[/tex] cross multiply
[tex]x^2=(25)(9)\to x=\sqrt{(25)(9)}\\\\x=\sqrt{25}\cdot\sqrt9\\\\x=5\cdot3\\\\x=15[/tex]
