Answer:
[tex]\huge\boxed{x=\sqrt{30}}[/tex]
Step-by-step explanation:
ΔABC and ΔBDC are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]
substitute
[tex]AC=7+3=10\\{BC}=x\\CD=3[/tex]
[tex]\dfrac{10}{x}=\dfrac{x}{3}[/tex] cross multiply
[tex](10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}[/tex]
