Question

If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square

Answer 1

Here we apply the Pythagorean theorem:
c^2=a^2+b^2
The diagonal of the opening will be:
c^2=3^2+3^2
c^2=9+9
c^2=18
c=3√2 ft

The diagonal of the wood will be:
c^2=4^2+8^2
c^2=16+64
c^2=80
c=4√5 ft

The space will not be enough for the plywood to pass