Carrying an object up the stairs

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Calculating whether a sofa can fit through bends in a staircase involves understanding the dimensions of both the sofa and the staircase. When faced with tight corners, lifting the sofa to position the longest side upward may provide a solution. However, the varying widths of the staircase before and after the bend complicate the calculations. A diagram can be a helpful tool to visualize the problem and determine if the sofa can navigate the turns. Proper measurements and angles are crucial for a successful outcome.
vega32
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Hi all,
I've got a question that came up while while carrying a sofa up the stairs. Is there a way that one could calculate whether or not the sofa (for the sake of simplifying, let's say that we're actually carrying a block -that wouldn't be far from the truth, given that the sofa remains in the cardboard container) would fit through the perpendicular bends in the stairway? OK, if the sofa is obviously not going to fit through, there is little point of even breaking a sweat doing the math, but nevertheless...

When one carries a sofa, the last resort at going through the bends is to lift the sofa up, so the longest side is facing up. Even if I disregard the height of the staircase, I still can't figure out the answer.

And too spice things up a bit, let's say that the staircase's width is wider before and narrower after the bend like in the attached picture.

I'd really appreciate your help.

Thanks!
 

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How would you get started on the problem? Suggestion --- draw a diagram (that includes the rectangle)
 

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