Question 1196831
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If two opposite sides of a square are increased by 8m. and the other 2 sides 
are decreased by 4 m. the area of the rectangle formed is 133 m^2. 
Find the area of the original square.
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<pre>
Your basic equation is

    (x+8)*(x-4) = 133  m^2.    (1)


Reduce to the standard form quadratic equation and solve it by any method you want.
</pre>

At this point, &nbsp;you have all necessary instructions to complete the solution on your own.



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Another method to solve it &nbsp;MENTALLY &nbsp;is to introduce new variable 


<pre>
          y = x+2.


Then  x+8 = y+6   and x-4 = y-6,

so equation (1) takes the form

    (y+6)*(y-6) = 133,


which implies

    y^2 - 36 = 133

    y^2      = 133 + 36 = 169

    y                   = {{{sqrt(169)}}} = 13.


Therefore,  x = 13-2 = 11.


The side of the original square is 11 m, and its area is {{{11^2}}} = 121 m^2.
</pre>

The possibility to find so unexpected elegant solution makes the Math more interesting.