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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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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.
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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 = = 13.
Therefore, x = 13-2 = 11.
The side of the original square is 11 m, and its area is = 121 m^2.
The possibility to find so unexpected elegant solution makes the Math more interesting.