Arectangle has an area of 209 square feet. the sides of the rectangle measure (4x-5) feet and (4x+3) feet. find the dimensions me with this question, is there any formula?

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


Combine like terms:

209 = 16x² - 8x - 15


Take away 209 from both sides :

0 = 6x² - 8x - 224


Switch Sides :

16x² - 8x - 224 = 0


Divide by 8 through :

2x² - x - 28 = 0


Factoise :

(2x + 7) (x - 4) = 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


The dimensions are 11 ft by 19 ft.