Question 14
Let $\triangle ABC$ be a right triangle with $\angle A = 90^\circ$ and $BC = 38.$ There exist points $K$ and $L$ inside the triangle such that $$
\begin{gathered} AK = AL = BK \\ = CL = KL = 14. \end{gathered}
$$ The area of the quadrilateral $BKLC$ can be expressed as $n\sqrt{3}$ for some positive integer $n.$ Find $n.$
\begin{gathered} AK = AL = BK \\ = CL = KL = 14. \end{gathered}
$$ The area of the quadrilateral $BKLC$ can be expressed as $n\sqrt{3}$ for some positive integer $n.$ Find $n.$