Question

A square ceiling has a diagonal of 24 ft. Shelton wants to put molding around the perimeter of the ceiling.

Answer 1

Square has all perimeter lines identical. to find the length of a side you can use a^2 = b^2 + c^2
24^2 = 576

as b and c are equal you can just divide 576 by 2 to get 288.
square root of 288 = 16.97 feet 

Answer 2

Square has legnth and width equal

if we draw a line from one cornder to the other, we get the diagonal
we also get 2 right triangles with diagonal=hyposonuse

and the sides of the room are the legs
since squae has all sides equal
legs are equall

a^2+b^2=c^2
a and b are legs
c=hyposonuse
a=b
a^2+a^2=c^2
c=24
2a^2=24^2
2a^2=576
divide 2
a^2=288
sqrt both sides
a=12√2

periimiter=4a
P=4*12√2
P=48√2 ft