Given:
A figure of a right angle triangle.
To find:
The value of x.
Solution:
First, label the vertices figure as shown below.
In triangle ABC and DBA,
[tex]\angle BAC\cong \angle BDA[/tex] (Right triangles)
[tex]\angle ABC\cong \angle DBA[/tex] (Common angle)
[tex]\triangle ABC\sim \triangle DBA[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional.
[tex]\dfrac{BC}{BA}=\dfrac{AB}{DB}[/tex]
Substituting the given values from the below figure, we get
[tex]\dfrac{x}{8\sqrt{3}}=\dfrac{8\sqrt{3}}{12}[/tex]
[tex]x=\dfrac{8\sqrt{3}}{12}\times 8\sqrt{3}[/tex]
[tex]x=\dfrac{192}{12}[/tex]
[tex]x=16[/tex]
Therefore, the value of x is 16 and correct option is B.
