MHB Prove Quadrilateral ABCD Perimeter $\geq (4+2\sqrt 2)S$

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A convex quadrilateral ABCD with area $S^2$ , prove the sum of its perimeter and two diagonal lines $\geq (4+2\sqrt 2)S$
 
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Albert said:
A convex quadrilateral ABCD with area $S^2$ , prove the sum of its perimeter and two diagonal lines $\geq (4+2\sqrt 2)S$
hint:
$Use\,\,area\,\,of \,\,a\,\,triangle=\dfrac {bc\,sin \,A}{2}=---,and\,\, AP\geq GP$
 

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