Final answer:
To find the length and width of the soccer field, we can set up a system of equations based on the given information. Solving this system of equations will give us the values of the length and width. The length of the soccer field is 96 yards and the width is 65 yards.
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the given information. Let's say the length of the soccer field is L yards and the width is W yards. We are told that the width is 17 yards more than half the length, so we can write the equation W = (1/2)L + 17. The perimeter of a rectangle is given by the formula P = 2L + 2W, so we can write the equation 322 = 2L + 2W.
Now we can solve this system of equations to find the values of L and W. Substituting the first equation into the second equation, we get 322 = 2L + 2((1/2)L + 17), which simplifies to 322 = 2L + L + 34. Combining like terms, we have 322 = 3L + 34. Subtracting 34 from both sides, we get 288 = 3L. Dividing both sides by 3, we find L = 96.
Substituting the value of L back into the first equation, we can solve for W. W = (1/2)(96) + 17, which simplifies to W = 48 + 17 = 65. Therefore, the length of the soccer field is 96 yards and the width is 65 yards.