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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