The Astute Ant

Geometry Level 4

In the figure we are shown a L-shaped block, with side-lengths $$2\text{ cm}$$.

An ant initially at point $$A$$, wants to go to point $$B$$, along the shortest path possible along the surface of the block.

If the length of the shortest path can be written as $$\sqrt{m}+\sqrt{n}$$ where $$m$$ and $$n$$ are square-free positive integers, find $$m+n$$.

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