Question

A soccer field is bordered on three sides by a parking lot of a width x. the total length of the field and parking lot is 300 M and a total width is 200 M the area of the field is 30000 M squared how wide is the parking lot

Answer 1

Answer: Parking lot is 60m wide

Explanation:

Since the parking lot is x meters, the length of the field would simply be (300-2x)m while the width of the field would be (200-x). The width would also have been 200-2x but we must remember that the field is only covered on 3 sides.

Area of the field is 30,000. This means if we multiply both, we get 30,000.

Mathematically;

(300-2x)(200-x) = 30,000

60,000-300x-400x+ 2x^2 = 30,000

2x^2-700x-30,000= 0

We can see we now have a quadratic equation we need to solve.

2x^2+500x-1200x-30,000= 0

2x(x+250) -120(x+250) = 0

(2x-120)(x+250) = 0

2x-120= 0 or x+250=0

2x = 120or x = -250

x = 120/2 or x= -250

x = 60 or x=-250

We discard x = -100 as x is length and cannot be negative

Hence, x = 60m