Answer:
[tex]\large\boxed{X=\sqrt{12}\ in=2\sqrt3\ in}[/tex]
Step-by-step explanation:
ΔADC and ΔCBD are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]
We have
AD = 2, CD = X, DB = 6.
Substitute:
[tex]\dfrac{2}{X}=\dfrac{X}{6}[/tex] cross multiply
[tex]X^2=(2)(6)\\\\X^2=12\to X+\sqrt{12}[/tex]
[tex]\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3[/tex]
