Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:
l = 3w + 4 (the length is 4 yards longer than triple the width)
We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:
P = 2l + 2w
We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:
416 = 2(3w + 4) + 2w
Simplifying and solving for w:
16 = 6w + 8
8 = 6w
w = 8/6 = 4/3
We can now substitute that back into the equation for the length:
l = 3w + 4
l = 3(4/3) + 4
l = 4 + 4
l = 8
So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.
Explanation: