Final answer:
The width of the pasture is found by setting up the equation 4w² = 2,230,400 ft², dividing by 4, and taking the square root of the result. The calculated width of the pasture is 747 feet.
Step-by-step explanation:
We need to find the width of a pasture where the length is four times the width, and the area of the pasture is 2,230,400 ft². First, let's denote the width as 'w' and the length as '4w' since the length is four times the width. The area of a rectangle is given by the formula Area = length × width. So in this case, the area is 2,230,400 ft² which equals to w × 4w.
We set up the equation 4w² = 2,230,400 ft². To find the width 'w', we need to divide both sides by 4, giving us ² = 557,600. Taking the square root of both sides, we find that w = √(557,600). We then find that w = 747 ft, which represents the width of the pasture.