Question

Find the value of x round to the nearest tenth if needed

Answer 1

The correct option is B. The value of x is 15.9.

Explanation:

From the given figure it is noticed that we have three right angle triangle.

In triangle ABC and ABD,

`\angle BAC=\angle BDA=90^(\circ)` (Given)

`\angle ABC=\angle DBA` (Common angle)

By AA rule of similarity,

`\triangle ABC\sim \triangle DBA` ... (1)

In triangle ABC and DAC,

`\angle BAC=\angle ADC=90^(\circ)` (Given)

`\angle ACB=\angle DCA` (Common angle)

By AA rule of similarity,

`\triangle ABC\sim \triangle DAC` ... (2)

Using (1) and (2),

`\triangle DBA\sim \triangle DAC` (Transitive property of similarity)

`(BD)/(AD)=(AD)/(CD)`

`(12)/(x)=(x)/(21)`

`x^2=12* 21`

`x=√(252)`

`x=15.8745\approx 15.9`

Therefore correct option is B. The value of x is 15.9.