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UKMT Mathematical Olympiad for Girls, 2021

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a quadrilateral $ABCD$ , where $AB$ is $2$ cm and $\angle ABC$ , $\angle ACD$ and $\angle DAB$ are right angles. Given that the area of quadrilateral $ABCD$ is $6\text{ cm}^2$ , find all possible values for the perimeter of quadrilateral $ABCD$ .

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