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 45-45-90 triangle since it is a square

Answer 1

The first step is to calculate the length of the diagonal of the square opening.

The length of a diagonal of square = $\sqrt{2}$ * side

Given side = 3 feet

Length of the square hole = $\sqrt{2}$ *3 = 4.24 feet

since the diagonal is 4.24 feet and the shorter side of the plywood piece is only 4 feet, we can slide it through the square hole diagonally

Answer is YES since the diagonal 4.24 feet is greater than the shorter side of the plywood piece *4 feet

Answer 2

THe diagonal of the 3*3 square = 3* sqrt2 = 4.24 feet   so the answer is Yes.