Question

Solve for x. Thank you

Answer 1

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,

$\angle BAC\cong \angle BDA$         (Right triangles)

$\angle ABC\cong \angle DBA$         (Common angle)

$\triangle ABC\sim \triangle DBA$         (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional.

$\dfrac{BC}{BA}=\dfrac{AB}{DB}$

Substituting the given values from the below figure, we get

$\dfrac{x}{8\sqrt{3}}=\dfrac{8\sqrt{3}}{12}$

$x=\dfrac{8\sqrt{3}}{12}\times 8\sqrt{3}$

$x=\dfrac{192}{12}$

$x=16$

Therefore, the value of x is 16 and correct option is B.