A square has one dimension increased by 4 feet and another dimension decreased by 2 feet. If the resulting rectangle has an area of 72 square feet, which of the following equations could be used to solve for the square's original side length, x?

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Answer 1 · 2018-03-26T05:08:53

Let the side of the square be #x# feet

One side is increased by 4 feet #=> x+4# feet

Other side is decreased by 2 feet.#=> x-2# feet

area of resulting rectangle #=> 72 # sq feet

#=> (x+4)(x-2) = 72#
#=> x^2 +4x -2x - 8 =72#
#=> x^2 +2x - 80 =0#
#=> x^2 +10x -8x- 80 =0#
#=> x(x +10) -8(x+ 10) =0#
#=> (x+10)(x-8) = 0#

therefore, #x=8 or -10#

since length cant be negative, #x=8#

Side of the square is 8 feet.