Answer:
x = 12
Step-by-step explanation:
ΔADC and ΔCDB are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{AD}{DC}=\dfrac{DC}{DB}[/tex]
We have AD = 16, DC = x, DB = 9. Substitute:
[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex] cross multiply
[tex]x^2=(16)(9)\to x=\sqrt{(16)(9)}\\\\x=\sqrt{16}\cdot\sqrt9\\\\x=4\cdot3\\\\x=12[/tex]
