Is it possible to construct a quadrilateral ABCD in which AB=3cm, BC=4cm, CD=5.5cm, DA=6cm and BD=9cm? If not give reason

Yes, its possible to construct a quadrilateral with the given figures. If we draw a rough figure/diagram of the quadrilateral we can get a good idea what the quad may look like. As per me the resulting figure will look somewhat like a kite(will not have the properties of a kite, but will be a rough type of kite.) 
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Yes it is possible
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is it possible to construct a quadrilateral ABCD in which a b equal to 3 cm is equal to 4 cm is equal to 5.5 cm is equal to 6 cm and BD equal to 9 cm is not give reason
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