This is the concept of algebra, given that the room is 150 sq. feet, the dimensions of the room can be found as follows;
Suppose the room is a perfect square, the length=width= x ft
therefore the are will be:
area=length*width
=x*x=x^2 sq. ft
hence;
x^2=150
getting the square root of both sides we get:
sqrt x^2=sqrt150
x=sqrt150
x=12.248 ft
x=12 ft (to the nearest feet)