The line ${\ell }_1$ passes through the point $A(2,1)$ and has gradient $2$.

The line ${\ell }_2$ passes through the points $(7,4)$ and $(10,3)$.

Given that the lines intersect at the point $B$, find the length $AB$, giving your answer in the form $k\sqrt{5}$ for some $k\in \mathbb{N}$.

To find the point of intersection, you can use simultaneous equations on the equations of the lines.

Here is a diagram:

You will need to use the distance formula on the coordinates of $A$ and $B$. (The point $B$ has integer coordinates.)