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.
Answers
Given : length is 36 feet longer than its width the area of the floor is less than 2040 square feet
To Find : the width of the floor
and Length of Floor
Solution:
Let say Width of the Floor = W feet
length is 36 feet longer than its width
Length = W + 36 Feet
area of the floor is less than 2040 square feet
Area = Length x Width
= (W + 36) W
(W + 36) W < 2040
=> W² + 36W < 2040
=> W² + 36W + 18² < 2040 + 18²
=> (W + 18)² < 48.62
| W + 18 | < 48.62
=> -48.62 < W + 18 < 48.62
=> -66.62 < W < 30.62
Width can not be -Ve
Hence 0 < W < 30.62
Width is less than 30.62 feet
Length is less than 66.62 feet
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