Area of a Square:
The area of a square is the measure of the region enclosed by the square. It is calculated by multiplying the length of one side of the square by itself. In other words, if "s" is the length of a side of the square, then the area "A" is given by the formula A = s^2.

Given Information:
In this problem, we are given that the area of a square field is 425 square units and the length of each side of the square is 40 units.

Finding the Area of the Path:
To find the area of the path, we need to subtract the area of the square field from the area of the larger square that includes the field and the path. Let's assume the width of the path is "w".

1. Area of the larger square:
The length of each side of the larger square is equal to the length of the side of the square field plus twice the width of the path. So, the length of each side of the larger square is (40 + 2w) units. Therefore, the area of the larger square is (40 + 2w)^2 square units.

2. Area of the field:
The area of the field is given as 425 square units.

3. Area of the path:
The area of the path is the difference between the area of the larger square and the area of the field. So, we can write the equation:
(40 + 2w)^2 - 425 = 0

Solving the Equation:
We can solve the quadratic equation to find the width of the path.

1. Expand the equation:
1600 + 160w + 160w + 4w^2 - 425 = 0

2. Simplify the equation:
4w^2 + 320w + 1600 - 425 = 0
4w^2 + 320w + 1175 = 0

3. Solve the equation:
Using the quadratic formula, we get:
w = (-b ± √(b^2 - 4ac)) / (2a)
where a = 4, b = 320, and c = 1175

Calculating the values using the formula, we find:
w = (-320 ± √(320^2 - 4 * 4 * 1175)) / (2 * 4)

After calculations, we find two possible values for the width of the path, which are approximately -49.7 and 7.2. Since the width cannot be negative, the width of the path is 7.2 units.

Therefore, the width of the path is 7.2 units.