------------------------------------------------------------- Formula for Area : ------------------------------------------------------------- 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)
------------------------------------------------------------- Expand the quadratic using FOIL: ------------------------------------------------------------- 209 = 16x² + 12x - 20x - 15
------------------------------------------------------------- Divide by 8 through : ------------------------------------------------------------- 2x² - x - 28 = 0
------------------------------------------------------------- Apply zero product property: ------------------------------------------------------------- 2x + 7 = 0 or x - 4 = 0 x = -7/2 (rejected) or x = 4
------------------------------------------------------------- Find the 2 sides : ------------------------------------------------------------- (4x - 5) = (4(4) - 5) = 11 ft (4x + 3) = (4(4) + 3) = 19 ft
------------------------------------------------------------- Answer: The dimensions are 11 ft by 19 ft. -------------------------------------------------------------
