SOLUTION: 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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Question 1196831: 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.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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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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.

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


                         * * * * *


Another method to solve it  MENTALLY  is to introduce new variable 

          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%28169%29 = 13.


Therefore,  x = 13-2 = 11.


The side of the original square is 11 m, and its area is 11%5E2 = 121 m^2.

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



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Using formal algebra (which is probably what you were asked to do...)

x = side of original square

x+8 and x-4 are side lengths of rectangle

The area of the rectangle is 133:

%28x%2B8%29%28x-4%29=133
x%5E2%2B4x-32=133
x%5E2%2B4x-165=0
%28x%2B15%29%28x-11%29=0
x=-15 or x=11

Clearly the negative solution makes no sense in the problem, so the side length of the square was 11m.

ANSWER: area of original square = 11^2 = 121 square meters

(2) Using simple mental arithmetic...

133 = 7(19) = (11-4)(11+8)