Question

On hypotenuse $AB$ of a right triangle $ABC$ a second right triangle $ABD$ is constructed with hypotenuse $AB$. If $\overline{BC}=1,\overline{AC}=b$, and $\overline{AD}=2$, then $\overline{BD}$ equals.

• A. $\sqrt{b^2+1}$
• B. $\sqrt{b^2-3}$
• C. $\sqrt{b^2+1}+2$
• D. $b^2+5$
• E. $\sqrt{b^2+3}$

Answer 1

The correct option is B $\sqrt{b^2-3}$

$x^2+4=b^2+1$
$\therefore x=\sqrt{b^2-3}$.