In triangle $ABC$, the median from vertex $A$ is perpendicular to the median from vertex $B$. If the lengths of sides $AC$ and $BC$ are $6$ and $7$ respectively, then the length of side $AB$ is
$\text{(A) } \sqrt{17}\quad \text{(B) } 4\quad \text{(C) } 4\tfrac{1}{2}\quad \text{(D) } 2\sqrt{5}\quad \text{(E) } 4\tfrac{1}{4}$
$\fbox{A}$
let the midpoint be M,N ( i.e. AM,BN are the medians); connecting MN we know that AB = 2x and MN = x hence apply stewart's theorem in triangle ABC with median MN first and then apply stewart's in triangle BNC with median MN