SOLUTION: A landscape designer has to design a retangular pad of concrete at the centre of a rock garden. The length must be less than or equal to twice the width; the perimeter must be less

>>......The length must be less than or equal to twice the width...<<

L < 2W

>>...the perimeter must be less than or equal to 40m...<<

Perimeter = 2L + 2W < 40

>>......and the area must be greater than or equal to 60m^2...<<

Area = LW > 60

So we have these three facts:

1.   L < 2W
2.   2L + 2W < 40
3.   LW > 60

Solve #2 for 2W:  2W < 40 - 2L

Putting this together with #1: 

L < 2W < 40 - 2L

Add 2L to all three sides:    

3L < 2W + 2L < 40

So  
     3L < 40

4.   L < 

Solve #3 for L:               

     L > 

or  < L 

Put that together with #4

 < L <  

So

 < 
  
        60 < W

       180 < 40W

    < W  
  
       < W

or            W >  

So since L <  and  W > 

The length must be less than or equal to 13 m.
The width must be greater than or equal to 4 m.

Edwin