Using given facts, the length of the parking lot to be increased is given by: Option B: 20 feet.
<h3>How does area of a rectangle, and its length and width are related?</h3>
Area of a rectangle is the product of its length and width.
If a rectangle has length L units and width of W units, then
Area = L × W squared units.
<h3>How to find the solution to a standard quadratic equation?</h3>
Suppose the given quadratic equation is
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
Then its solutions are given as
![x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
For the given case, we can use variable in place of unknown increment in length and width of the parking lot.
- Current length of the parking lot = 120 ft
- Current width of the parking lot = 80 ft.
Thus, current area of the parking lot = ![120 \times 80 = 9600 \:\rm ft^2](https://tex.z-dn.net/?f=120%20%5Ctimes%2080%20%3D%209600%20%5C%3A%5Crm%20ft%5E2)
Let the increment in length and width of the parking lot be of 'x' feet.
Then, we get:
- New length of the parking lot = 120 + x ft.
- New width of the parking lot = 80 + x ft.
Thus, new area of the parking lot = ![(120 + x)(80 +x )](https://tex.z-dn.net/?f=%28120%20%2B%20x%29%2880%20%2Bx%20%29)
It is given that the new area = current area + 4400 ft squared.
Thus, we get an equation as:
![(120 + x)(80 +x ) = 9600 + 4400 = 14000\\9600 + 200x + x^2 = 14000\\x^2 + 200x -4400 = 0\\](https://tex.z-dn.net/?f=%28120%20%2B%20x%29%2880%20%2Bx%20%29%20%3D%209600%20%2B%204400%20%3D%2014000%5C%5C9600%20%2B%20200x%20%2B%20x%5E2%20%3D%2014000%5C%5Cx%5E2%20%2B%20200x%20-4400%20%3D%200%5C%5C)
Comparing it with
, we get a = 1, b = 200, c = -4400
Thus, its roots are:
![x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-200 \pm \sqrt{(200)^2 - 4(-4400)(1)}}{2} = \dfrac{-200 \pm \sqrt{57600}}{2}\\\\x = \dfrac{-200 \pm 240}{2} \\\\x = -220, x = 20](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%20%3D%20%5Cdfrac%7B-200%20%5Cpm%20%5Csqrt%7B%28200%29%5E2%20-%204%28-4400%29%281%29%7D%7D%7B2%7D%20%3D%20%5Cdfrac%7B-200%20%5Cpm%20%5Csqrt%7B57600%7D%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20%5Cdfrac%7B-200%20%5Cpm%20240%7D%7B2%7D%20%5C%5C%5C%5Cx%20%3D%20-220%2C%20%20x%20%3D%2020)
x is denoting the length increased, so it cannot be negative, as increment is in positive sign always.
Thus, x = 20 (feet).
Learn more about solution of quadratic equations here:
brainly.com/question/3358603