## 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

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 m2. How wide is the parking lot

in progress 0
4 weeks 2021-09-16T01:30:58+00:00 2 Answers 0

Step-by-step explanation:

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

Parking lot is 60m wide

Step-by-step explanation:

In this question. We are asked to calculate the width of the parking lot. We proceed as follows:

We know that the total length of the field and the parking lot is 300m while the total width is 200m. We should remember that the field is rectangular in nature.

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