Question 1170073
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W = width
W+10 = length, since it is 10 meters longer than the width


Area = Length*Width
Area = (W+10)*W
Area = W^2+10W


The area is greater than 600 square meters, so,


Area > 600
W^2+10W > 600
W^2+10W-600 > 0
(W+30)(W-20) > 0


There are two ways to have the factors (W+30) and (W-20) multiply to a positive value


Case 1: Both factors (W+30) and (W-20) are positive
Case 2: Both (W+30) and (W-20) are negative



Let's focus on case 1
If W+30 > 0, then W > -30
If W-20 > 0, then W > 20
If both are the case, then W > 20 which is what both intervals have in common.


Now move onto case 2
If W+30 < 0, then W < -30
If W-20 < 0, then W < 20
Those two intervals overlap over W < -30 since something like W = -35 is in both intervals.
However, we can't have negative widths. So case 2 in its entirety is going to be ignored.



Therefore, the only possible values of W are ones such that W > 20. 
In words: the width must be larger than 20.


Let's say the width was W = 25 meters
This makes the length to be W+10 = 25+10 = 35 meters
The resulting area is length*width = 35*25 = 875 square meters, which exceeds 600 square meters.


One possible dimension of the floor is 25 meters by 35 meters, which has an area of 875 square meters.


There are infinitely more possible answers since all that matters is W > 20.
So you could have W = 30, W = 40, etc
There is no upper bound. Though in a realistic sense, you'll run out of room eventually. At the same time, we can still pick infinitely many values between two fixed points. For example, there are infinitely many numbers between W = 30 and W = 40 if we include all real numbers, and not just whole numbers. 


If your teacher made a restriction like "W is whole number between 21 and 30", then we would have finitely many values of W and therefore finitely many answers. However, this isn't the case here.

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