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Is it possible to fit through this gap

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Just make some 1:10 scale models and play with them. Or better yet, just play with a few pieces of paper and see if you can “fit” them into a shape. Then consider *generally* why things fit or didn’t fit. How could you describe how you tilted them mathematically?

Don’t forget your Pythagorean theorem!

Hint: if you tilt an object to fit through a door, does the object need to be the same width or smaller than the door, or does something else need to be the same width or smaller?
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It sounds like you're saying the cross-section is an L-shape. It would probably be necessary to give more details on the cross-section to answer. It could conceivably also depend on whether you have all the room you might want on both sides of the door.

In any case, your best bet will probably be to try to slide it through standing on end and manoevring the L through the door, rotating it as you go.

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