Final answer:
The width of the farmer's rectangular field is determined using the Pythagorean theorem. It turns out to be 60 yards after calculating the square root of 3600, which we got by subtracting the square of the field's length from the square of the distance between opposite corners.
Step-by-step explanation:
To find the width of the farmer's rectangular field, we can use the Pythagorean theorem, which applies to right triangles. The formula for the Pythagorean theorem is a² + b² = c², where c is the length of the hypotenuse (longest side of the triangle), and a and b are the lengths of the other two sides.
In this scenario, the field's length (a) is 80 yards and the distance between opposite corners (c, or the hypotenuse) is 100 yards. We want to find the width of the field (b). Setting up the equation, we have:
80² + b² = 100²
Calculating each term gives us:
6400 + b² = 10000
Next, we subtract 6400 from both sides to solve for b²:
b² = 10000 - 6400
b² = 3600
To find b, we take the square root of both sides:
b = √3600
b = 60 yards
Therefore, the width of the farmer's field is 60 yards.