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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.

Respuesta :

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.



abidemiokin
  • L < 66; The length of the floor will be less than 66feet

  • W<30; The width of the floor will be less than 30feet

  • The possible area of the floor is 1885 sq. ft

  • Since 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft

The formula for calculating the area of the conference floor is expressed as:

A = LW

L is the length

W is the width

If the length is 36ft. longer than its width, hence;

L = W+36

Since the area of the floor is less than 2040 square feet, hence;

A < 2040

LW < 2040

(W+36)W < 2040

W² + 38W < 2040

W² + 38W - 2040 < 0

W² + 68W - 30W - 2040 < 0

W(W+68)- 30(W+68)< 0

(W-30)(W+68) < 0

W - 30 < 0 and W < -68

W < 30

Since the width cannot be negative, hence the width of the floor will be less than 30feet

Since L = 36 + W

L < 36 + 30

L < 66feet

The length of the floor will be less than 66feet

The possible dimensions area 29feet by 65feet since the width is less than 30 and the length is less than 66feet.

Get the possible area:

Possible area = 29 × 65

Possible area = 1885feet²

Since 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft

Learn more here: https://brainly.com/question/21067938

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