Answer:
The correct option is B. The value of x is 15.9.
Step-by-step explanation:
From the given figure it is noticed that we have three right angle triangle.
In triangle ABC and ABD,
[tex]\angle BAC=\angle BDA=90^{\circ}[/tex] (Given)
[tex]\angle ABC=\angle DBA[/tex] (Common angle)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle DBA[/tex] ... (1)
In triangle ABC and DAC,
[tex]\angle BAC=\angle ADC=90^{\circ}[/tex] (Given)
[tex]\angle ACB=\angle DCA[/tex] (Common angle)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle DAC[/tex] ... (2)
Using (1) and (2),
[tex]\triangle DBA\sim \triangle DAC[/tex] (Transitive property of similarity)
[tex]\frac{BD}{AD}=\frac{AD}{CD}[/tex]
[tex]\frac{12}{x}=\frac{x}{21}[/tex]
[tex]x^2=12\times 21[/tex]
[tex]x=\sqrt{252}[/tex]
[tex]x=15.8745\approx 15.9[/tex]
Therefore correct option is B. The value of x is 15.9.
