Tough Perimeter

Geometry Level 3

Here in \( \triangle ABC\) , \( AC=4 \text {units} , \angle ABC=90^{\circ} \) and \(BDEF\) is a square of side length 1 unit. The perimeter of the \( \triangle ABC\) can be written as \( \sqrt {m } + n \) where \(m\) and \(n\) are non-negative integers.What is the value of \(m+n\)?

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