SOLUTION: Alex wants to build a rectangular garden enclosed with a fence. He wants the length of the garden to be 5 meters longer than the width. If the area of the garden must be less than

Let x be the smaller dimension, in meters (the width).

Then the larger dimension (the length) is (x+5) meters, according to the condition.



They want you determine x in a way to satisfy inequality

    x*(x+5) < 14.


It is equivalent to 

    x^2 + 5x - 14 < 0,


or, in factored form

    (x+7)*(x-2) < 0.


The solution to this inequality is the set

    -7 < x < 2.


But due to meaning of x, the dimension x must be positive.


Therefore, the final solution is the set of real numbers  0 < x < 2 meters.


ANSWER.  The width must be shorter than 2 meters;  the length is 5 meters greater than the width.