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Formula for Area :
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Area = Length x Width
Since we know that the area is 209 ft² and the sides are (4x-5)ft and (4x+3) ft, we will plug in these values and solve for x.
209 = (4x-5)(4x + 3)
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Expand the quadratic using FOIL:
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209 = 16x² + 12x - 20x - 15
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Combine like terms:
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209 = 16x² - 8x - 15
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Take away 209 from both sides :
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0 = 6x² - 8x - 224
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Switch Sides :
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16x² - 8x - 224 = 0
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Divide by 8 through :
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2x² - x - 28 = 0
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Factoise :
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(2x + 7) (x - 4) = 0
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Apply zero product property:
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2x + 7 = 0 or x - 4 = 0
x = -7/2 (rejected) or x = 4
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Find the 2 sides :
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(4x - 5) = (4(4) - 5) = 11 ft
(4x + 3) = (4(4) + 3) = 19 ft
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Answer: The dimensions are 11 ft by 19 ft.
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