Intersection Mania

Geometry Level 3

Give ABC is a triangle have \(AB=k;\quad \widehat { BAC } ={ 60 }^{ \circ };\quad \widehat { ACB } ={ 45 }^{ \circ };\quad AD\bot BC\quad (D\in BC);\quad \\ BE\bot AC\quad (E\in AC);\quad CF\bot AB\quad (F\in BA)\) . Calculated according to \(k\), the perimeter of \(\Delta ABC\) is:

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