The mattress can fit through the door.
The door is 78 inches tall and 38 inches wide. If you do the Pythagorean theorem with these numbers you get the hypotenuse of 86.76, which is larger than the width of the mattress.
38^2+78^2=c^2
1444+6084=7528
Take square root of 7528, which is 86.76
