Folds and Creases-1

Geometry Level 5

A piece of paper is in the form of an equilateral triangle \(ABC\) with side length \(a\). A fold is made such that vertex \(A\) of the triangle meets a point \(D\) on \(AC\) such that \(AD=\dfrac{a}{3}\). Find the value of \(k\), if the perimeter of the resulting concave quadrilateral is \(ka\).

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