Question

A field has a walkway surrounding it by 3 sides. The total width/base of the area, both the field and walkway, is 300m while the total length is 200m. The area of the field is 30,000m and the total area is 60,000m. The thickness/width of the walkway is x, what does x equal?

Answer 1

x = 15.

Therefore, the width of the walkway is 15m.

Explanation:

Let's represent the width of the walkway by "x".

We know that the total width/base of the area (including the walkway) is 300m, so we can set up the equation:

length of field + 2(width of field) + 2(width of walkway) = 300

Substituting the given values, we get:

200 + 2w + 2x = 300

Simplifying the equation, we get:

2w + 2x = 100

We also know that the area of the field is 30,000m, so we can set up the equation:

length of field x width of field = 30,000

Substituting the given values, we get:

200w = 30,000

Simplifying the equation, we get:

w = 150

Finally, we know that the total area (including the walkway) is 60,000m, so we can set up the equation:

(length of field + 2x) x (width of field + 2x) = 60,000

Substituting the values we've found so far, we get:

(200 + 2x) x (150 + 2x) = 60,000

Expanding the equation, we get:

300x^2 + 1000x - 45,000 = 0

Solving for x using the quadratic formula, we get:

x = 15 or x = -30/100

Since x can't be negative, we can discard the negative solution and conclude that x = 15.

Therefore, the width of the walkway is 15m.