Does the couch fit through the door?

Geometry Level 2

Peter has ordered a new couch for his TV room, which has a rectangular L-shape as a cross-section. The piece of furniture is 220 cm long, 98 cm wide, and 77 cm high. In addition, the padding has a thickness of 14 cm.

Now Peter notices that the opening of his room door is only 70 cm wide and 180 cm high.

Does the couch still fit through the door anyway?

Assumptions: The couch can be rotated arbitrarily. It fits through the door if its cross-section lies completely in the rectangle of the door frame. Additional wiggle room is not necessary.

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