Question 13
In triangle $ABC,$ $AB=\sqrt{30},$ $AC=\sqrt6,$ and $BC=\sqrt{15}.$ There is a point $D$ for which $\overline{AD}$ bisects $\overline{BC},$ and $\angle ADB$ is a right angle. The ratio $$
\frac{\operatorname{Area}(\triangle ADB)}{\operatorname{Area}(\triangle ABC)}
$$ can be written in the form $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$
\frac{\operatorname{Area}(\triangle ADB)}{\operatorname{Area}(\triangle ABC)}
$$ can be written in the form $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$