Question 1134826
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            Let me show you the way that you,  probably,  NEVER  HEARD  and  SEEN.



<pre>
W is the width;  (2W-12) is the length.


The area equation is

    W*(2W-12) = 2574.       (1)


Multiply both sides by 2 to get

    2W*(2W-12) = 5148.      (2)


Let x be the value midway between  2W  and  (2W-12)    (the arithmetic mean of the two expressions).


Then it is clear that  2W = x+6,  while  2W-12 = x-6.


Then the equation (2) becomes

    (x+6)*(x-6) = 5148

    x^2 - 36 = 5148

    x^2 = 5148 + 36 = 5184  ============>  x = {{{sqrt(5184)}}} = 72.


Then  2W = x+6 = 72 + 6 = 78,  hence,  W = 78/2 = 39   and   L = 2W-12 = 2*39 - 12 = 66.


<U>Answer</U>.  The length of the rectangle is 66 meters.
</pre>

Solved and completed.


Notice that the only "time consuming" step in my solution was to take the square root of  5184.   &nbsp;&nbsp;//  &nbsp;&nbsp;Ha-ha-ha.

<pre>
    (The rest can be done MENTALLY).
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To see how this method/idea works in other similar problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/How-to-solve-the-problem-on-quadratic-equation-mentally-and-avoid-boring-calculations.lesson>HOW TO solve the problem on quadratic equation mentally and avoid boring calculations</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Three-methods-to-find-the-dimensions-of-a-rectangle-when-the-givens-are-its-perimeter-and-the-area.lesson>Three methods to find the dimensions of a rectangle when its perimeter and the area are given</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Three-methods-to-find-the-dims-of-a-rectangle-when-its-area-and-the-diff-of-dims-are-given.lesson>Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given</A> 

in this site.


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Let me make my comment regarding the words by @greenestamps  "there is no advantage to using formal algebra".


<pre>
    All what we teach you in this site, is formal algebra and/or is based on formal algebra methods.


          Thanks to those intellectual giants who built this base . . . 


    If sometimes we tell you about possibilities to solve the problems mentally, it is not to convince you do not use formal algebra.


    We do it only to wider your horizon and/or to make your mind more flexible.


    So, do not consider these words by the esteem tutor @greenestamps too seriously . . . 


    Consider them in a "joking mode" . . . 
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