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.

`(BC)/(BA)=(AB)/(DB)`

Substituting the given values from the below figure, we get

`(x)/(8√(3))=(8√(3))/(12)`

`x=(8√(3))/(12)* 8√(3)`

`x=(192)/(12)`

`x=16`

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