Question 1186519
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Let x be one side of the rectangular garden, in meters.

Then the other (adjacent) side length is  48/2 - x = 24 - x meters long.


The expression for the area is  x*(24-x)  square meters.


The inequality, which you want to impose on dimensions (on the area) is


    108 <= x*(24-x) <= 150  square meters,


or, which is the same


    108 <= -x^2 + 24x <= 150.


The quadratic function  -x^2 + 24x  has the maximum value of 144, which is achieved at x = 12.

It is less than 150, so inequality  x^2 + 24x <= 150  is valid for ANY VALUE of x, without restrictions.



The inequality  108 <= -x^2 + 24x  is valid at  6 <= x <= 18.



So, one side of the rectangular garden MUST SATISFY this restrictions.


The other (adjacent) side should be (24-x) meters long.


    (By the way, then the other (adjacent) side satisfies the same restrictions/inequalities (!) )


There are INFINITELY MANY possibilities under these conditions.
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Solved.