Find the dimensions of the parking area if it must be 150,000 ft² where the width is 50 ft

more than a number and the length is 200 ft less than the width.

what would be the equation?

x² - 100x - 157500 = 0

Step-by-step explanation:

Let the number be x.

Width = x + 50

Length = x + 50 - 200 = x - 150

Area of parking lot = 150000

Length * Width = 150000

(x - 150) * (x + 50) = 150000

x * (x+50) - 150 * (x+50) = 150000

x² + 50x - 150x - 7500 = 150000

x² - 100x - 7500 - 150000 = 0

x² - 100x - 157500 = 0

(x+350) (x-450) = 0

x - 450 = 0 {x + 350 = 0 cannot be solution as x will take a negative value}

x = 450 ft

Length = x - 150 = 450 - 150 = 300 ft

Width = x + 50 = 450 + 50 = 500 ft