Answer:
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
