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2015-03-24T03:16:36+05:30

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Area of rectangular piece of paper = 12 * 9 = 108 cm²
a piece of width x cm is cut out from all sides of rectangle..
Width of the remaining piece of paper = 9 - 2 x cm
length of the remaining piece of paper = 12 - 2 x cm

The area of the remaining piece = (9 - 2x ) (12 - 2x) cm²
       = 108 - 42 x + 4 x²  = 54 cm²
  =>  2 x² - 21 x +27 = 0
        factors of 2 * 27 = 2, 3, 6, 9, 18, 27, 54 , 1
                     -18 - 3 sum to -21
         (2 x - 3 )(x - 9) = 0  =>  x = 1.5 cm or 9 cm
           x cannot be 9 cm.  Hence    x = 1.5 cm.

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Area of rectangular piece of paper = 12 * 9 = 108 cm²
a piece of width x cm is cut out from all sides of rectangle..
Width of the remaining piece of paper = 9 - 2 x cm
length of the remaining piece of paper = 12 - 2 x cm

The area of the remaining piece = (9 - 2x ) (12 - 2x) cm²
= 108 - 42 x + 4 x² = 54 cm²
=> 2 x² - 21 x +27 = 0
factors of 2 * 27 = 2, 3, 6, 9, 18, 27, 54 , 1
-18 - 3 sum to -21
(2 x - 3 )(x - 9) = 0 => x = 1.5 cm or 9 cm