The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The area of the resulting rectangle is #90 ft^2#. What is the original area of the square?

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Answer 1 · 2015-11-15T03:03:49

#A = 64 ft^2#

Let #x# be the length of one side of the square

#A_r = LW#
#L = x + 7#
#W = x - 2#

#(x + 7)(x - 2) = 90#

#=> x^2 + 5x - 14 = 90#

#=> x^2 + 5x - 104 = 0#

#=> (x + 13)(x - 8) = 0#

#=> x = -13, x = 8#

But since we're dealing with measurements here, the value should be positive.

#x = 8#

#A_s = S^2#

#=> A_s = x^2#

#=> A_s = 8^2#

#=> A_s = 64#