A little point

In $\triangle ABC$ let $AB=BC=L$ and $\angle ABC = 90°$ . There is a point $Q$ inside $\triangle ABC$ such that $QA=k$ , $QB=2k$ and $QC=3k$ . If $\left(\dfrac{L}{k}\right)^2=a+b\sqrt{c}$ , where $a$ , $b$ and $c$ are natural numbers and $c$ is prime, find $a+b+c$ .