Question

In a right angled triangle, altitude divides the hypotenuse into two segments of length $8$ and $18,$ then the length of the smallest side is
(correct answer + 1, wrong answer - 0.25)

• A. $8\sqrt{2}$
• B. $6\sqrt{13}$
• C. $4\sqrt{13}$
• D. $8\sqrt{3}$

Answer 1

The correct option is C $4\sqrt{13}$


$\angle ABD=\angle CAD=\theta$ and $\angle ADB=\angle ADC={90}^{\circ }$
$\Rightarrow \Delta ABD$ and $\Delta CAD$ are similar triangle.
$\therefore \frac{CD}{AD}=\frac{AD}{BD}$
$\Rightarrow \frac{8}{AD}=\frac{AD}{18}$
$\Rightarrow AD=12$
Now, smallest side, $AC=\sqrt{8^2+{12}^2}=4\sqrt{13}$