Final answer:
The width of the field is 56 yards and the length is 222 yards.
Step-by-step explanation:
To find the dimensions of the playing field, we can set up equations using the given information. Let's denote the width of the field as 'w' and the length as 'L'. We know that the perimeter of a rectangle is given by:
P = 2(w + L).
We are given that the perimeter is 556 yards, so we can write the equation as:
556 = 2(w + L). We are also given that the length is 2 yards less than quadruple the width, so we can write another equation as: L = 4w - 2.
Let's substitute the value of L from the second equation into the first equation:
556 = 2(w + (4w - 2)).
Simplifying this equation, we get:
556 = 10w - 4.
Adding 4 to both sides, we have:
560 = 10w. Dividing both sides by 10, we get:
w = 56. Now we can substitute the value of w back into the second equation to find L:
L = 4(56) - 2 = 224 - 2 = 222.
Therefore, the width of the field is 56 yards and the length is 222 yards. So option d) The width is 132 yards, and the length is 270 yards, is incorrect.