The value of[tex]x[/tex] is required.
The value of [tex]x[/tex] is 6.
Angle DBC and Angle DBA are equal.
BD is common side.
So, the triangles ABD and DBC are similar by Side Angle Side similarity.
This means the sides have a common ratio
[tex]\dfrac{6}{x+3}=\dfrac{4}{x}\\\Rightarrow 6x=4x+12\\\Rightarrow x=\dfrac{12}{6-4}=\dfrac{12}{2}\\\Rightarrow x=6[/tex]
The value of [tex]x[/tex] is 6.
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