The floor of a conference hall can be covered completly with tiles. its length is 36ft. longer than its width. the area of the floor is less than 2040square ft. how would you represent the with of the floor? how about its lenght? what mathematical sentence would represent the given situation? what are the possible dimensions of the floor? how about the possible areas of the floor? would it be realistic for the floor to have an area of 144sq. ft? explain your answer.

Let's start by defining a few variables:
x=width of the floor
x+36= length of the floor 
Since area = length x width, we can write the equation:
x(x+36)<2040 ft² (this is your mathematical sentence
Make a chart of the possible values:
x  | x+36|  Area
30   66  = 1980  fits
31   67  = 2077 *too big
So, all dimensions with length smaller than 30 and widths smaller than 66 fit the system. 
x(x+36)=144? Let's try smallest numbers - width of 1 ft, length of 37 ft
1(37)=37 too small
3(39)=117 nope
4(40)=160 nope
So, no, 144 ft² is not a realistic answer.