Moving Furniture: A Practical Riddle

For all of you math gurus out there, help me out: If you have a bed that is 6’10” tall, 4’10” wide, and 14” high, can it fit through a 6’7” tall, 2’5” wide doorway?

I know the solution should have something to do with a diagonal created by tilting the bed in the doorway, so that means we need to create two imaginary triangles out of the rectangle made by the doorway. (The diagonal, if I remember correctly from 8th grade geometry, is called the hypotenuse.) To do all of this, I guess we first have to convert everything to inches, so let's do that:

bed length = 82"

bed width = 58"

bed height = 14"

doorway height = 79"

doorway width = 29"

Okay, so now we have the equation a² + b² = c², with c² being the hypotenuse. (Pythagorean's theorem, if I am actually brushing the correct cobwebs off of these dusty old mathematical memories.) a = doorway height, b = doorway width (i.e. the floor, or the base of this triangle), and c = the imaginary diagonal that will, hopefully, be longer than the bed length.

√(6241 + 841)=84.15

Whew! So, if the diagonal is ~84" long, and the bed is 82" long, it will fit!

But wait.... Couldn't we have just turned the bed on its side--so that the width was essentially the length--and gotten it out the doorway like that?

Well, this was a fun mathematical exercise, nonetheless. Nothing like proving those 8th grade math skills were meant to come in handy after all!