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if the length of one side of a square is doubled and the length of an adjacent side is decreased by 3,
the area of the resulting rectangle exceeds the area of the original square by 16.
The length of a side of the original square is?
Let s = length of the side of the original square
s^2 = original area
and the new rectangle dimensions will be
2s by (s-3)
New area - old area = 16
2s(s-3) - s^2 = 16
2s^2 - 6s - s^2 = 16
2s^2 - s^2 - 6s - 16 = 0
s^2 - 6s - 16 = 0
(s-8)(s+2) = 0
s = 8 units, the length of the original square
Check this by finding the areas
16(8-3) = 80
8*8 = 64