Final answer:
To find the total cost of grassing the field, we need to determine its area and multiply it by the cost per square yard. The area of the field can be found by solving for the length and width using the given perimeter. Substituting these values into the area formula and multiplying by the cost per square yard gives the total cost of grassing the field.
Step-by-step explanation:
To find the total cost of grassing the field, we need to first determine the area of the rectangular soccer field. The perimeter of the field is given as 320.98 yards. Since the perimeter of a rectangle is the sum of all its sides, we can divide the perimeter by 2 and subtract the width from the result to find the length of the field. Then, we can calculate the area of the field by multiplying the length and width together. After finding the area, we can multiply it by the cost of covering the field with specialized grass per square yard to get the total cost of grassing the field.
Given that the perimeter of the field is 320.98 yards, let's assume the length is L and the width is W. We can write the equation: 2L + 2W = 320.98. Simplifying this equation, we get L + W = 160.49. Since the length is L and the width is W, we can rewrite this equation as L = 160.49 - W. Now, let's substitute this expression for L into the area formula. The area of the field is A = L * W = (160.49 - W) * W = 160.49W - W^2. The total cost of grassing the field is the area of the field multiplied by the cost of covering the field with specialized grass per square yard, which is $35.70. Therefore, the total cost of grassing the field is 35.70 * (160.49W - W^2).
To find the value of W, we can use the fact that the field is rectangular. Since the opposite sides of a rectangle are equal in length, we know that L = W. We can substitute L = W into the equation L + W = 160.49 and solve for W. 2W = 160.49, so W = 160.49 / 2 = 80.245.
Now, substitute this value of W into the formula for the area: A = (160.49 - 80.245) * 80.245 = 6431.237025. Finally, calculate the total cost of grassing the field: total cost = 35.70 * 6431.237025 = $229850.12.