word problem assistance please!

Question

A soccer field is bordered on three sides by a parking lot of width x. The total length of the field and parking lot is 300 m, and the total width is 200 m. The area of the field is 30,000 m^2. How wide is the parking lot?

Answer 1

Assuming the parking lot is along both widths of the field and only once along the length:

the length is (300 - 2x)

the width is (200 -x)

the area is (300-2x)(200-x) = 30000

60000 -300x - 400x +2x^2 = 30000

2x^2 -700x + 30000 = 0

x^2 - 350x + 15000 = 0

(x - 300 )(x - 50 ) = 0

x = 300 or x=50

x=300 results in negative measures.

the parking lot is x=50 wide

the length of the field is 200, the width of the field is 150