Question 1157163
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Let x an y be the dimensions of the base of the box.


Then the volume is  126 = 2*x*y, which implies

   xy = 126/2 = 63.    (1)


The dimensions of the original cardboard are (x+2*2) = x+4  and  (y+2*2) = y+4, and its area is, therefore

    (x+4)*(y+4) = 143.


Make FOIL

    xy + 4x + 4y + 16 = 143.


Substitute here  xy = 63  from (1), and you will get

    63 + 4x + 4y + 16 = 143,   

or

    x + y = {{{(143 - 63 - 16)/4}}} = 16.    (2)


So, you need to find two positive numbers, x and y, whose sum is 16  and whose product is 63.


4 seconds, and the solution just came into your mind:  x= 9  and  y= 7.


Then the original dimensions of the cardboard are  9+4 = 13 and  7+4 = 11 centimetres.    <U>ANSWER</U>
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Solved  // (practically, MENTALLY).