A square room means that all four sides of the room will be of equal length, and that each corner of the room will be a right angle measuring 90˚. The diagonal of the room forms a hypotenuse for a right triangle formed by one/half of the ceiling. Since we know that each side of the ceiling is equal to each other, we can use the pythagorean theorem to determine the missing side lengths.
c(squared) = a(squared) + b(squared)
24(squared) = a(squared) + b(squared)
576 divided by 2 (because the side lengths are the same) = 288
The square root of 288 = 16.97 so each side length is approx. 17' in length.
