# Tough Perimeter

Geometry Level 3

Here in $$\triangle ABC$$ , $$AC=4 \text {units} , DE= EF =1 \text {unit}, \angle ABC=90^{\circ}$$ and $$\angle DEF = 90^\circ$$. 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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