Question 1114583
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<pre>
Let x be the mean value between the length and the width.

Then the length is  (x+2) meters, while the width is  (x-2) meters


The area is L*W = (x+2)*(x-2) = {{{x^2-4}}}.


The condition gives the equation

x^2 - 4 = 26,


which implies  {{{x^2}}} = 26+4 = 30  ====>  x = {{{sqrt(30)}}}.


Then   the length = {{{2 + sqrt(30)}}} meters;  width = {{{sqrt(30)-2}}} meters.


<U>Check</U>.  The area =  {{{(sqrt(30)+2)*(sqrt(30)-2)}}} = 30 - 4 = 26.


<U>Answer</U>.  the length = {{{2 + sqrt(30)}}} meters;  width = {{{sqrt(30)-2}}} meters.
</pre>

Solved.


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To see other similar problems, solved by the same method, look into the lesson

&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> 

in this site.



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Why this method is good ? &nbsp;&nbsp;- &nbsp;&nbsp;Because it allows you to get the solution &nbsp;MENTALLY, &nbsp;without long and boring calculations.