<PRE><B>Question 117470</B>
 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 than or equal to 40m; and the area must be greater than or equal to 60m^2
&lt;pre&gt;&lt;b&gt;
&gt;&gt;......The length must be less than or equal to twice the width...&lt;&lt;

L &lt;u&gt;&lt;&lt;/u&gt; 2W

&gt;&gt;...the perimeter must be less than or equal to 40m...&lt;&lt;

Perimeter = 2L + 2W &lt;u&gt;&lt;&lt;/u&gt; 40

&gt;&gt;......and the area must be greater than or equal to 60m^2...&lt;&lt;

Area = LW &lt;u&gt;&gt;&lt;/u&gt; 60

So we have these three facts:

1.   L &lt;u&gt;&lt;&lt;/u&gt; 2W
2.   2L + 2W &lt;u&gt;&lt;&lt;/u&gt; 40
3.   LW &lt;u&gt;&gt;&lt;/u&gt; 60

Solve #2 for 2W:  2W &lt;u&gt;&lt;&lt;/u&gt; 40 - 2L

Putting this together with #1: 

L &lt;u&gt;&lt;&lt;/u&gt; 2W &lt;u&gt;&lt;&lt;/u&gt; 40 - 2L

Add 2L to all three sides:    

3L &lt;u&gt;&lt;&lt;/u&gt; 2W + 2L &lt;u&gt;&lt;&lt;/u&gt; 40

So  
     3L &lt;u&gt;&lt;&lt;/u&gt; 40

4.   L &lt;u&gt;&lt;&lt;/u&gt; {{{40/3}}}

Solve #3 for L:               

     L &lt;u&gt;&gt;&lt;/u&gt; {{{60/W}}}

or {{{60/W}}} &lt;u&gt;&lt;&lt;/u&gt; L 

Put that together with #4

{{{60/W}}} &lt;u&gt;&lt;&lt;/u&gt; L &lt;u&gt;&lt;&lt;/u&gt; {{{40/3}}} 

So

{{{60/W}}} &lt;u&gt;&lt;&lt;/u&gt; {{{40/3}}}
  
        60 &lt;u&gt;&lt;&lt;/u&gt; {{{40/3}}}W

       180 &lt;u&gt;&lt;&lt;/u&gt; 40W

   {{{180/40}}} &lt;u&gt;&lt;&lt;/u&gt; W  
  
      {{{9/2}}} &lt;u&gt;&lt;&lt;/u&gt; W

or            W &lt;u&gt;&gt;&lt;/u&gt; {{{9/2}}} 

So since L &lt;u&gt;&lt;&lt;/u&gt; {{{40/3}}} and  W &lt;u&gt;&gt;&lt;/u&gt; {{{9/2}}}

The length must be less than or equal to 13{{{1/3}}} m.
The width must be greater than or equal to 4{{{1/2}}} m.

Edwin&lt;/pre&gt;
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