Final answer:
The width of the rectangular playing field is 42 yards and the length is 129 yards.
Step-by-step explanation:
To find the dimensions of the rectangular playing field, we can set up an equation using the information given. Let's assume the width of the field is 'w'. According to the problem, the length is 3 yards longer than triple the width, so the length would be '3w + 3'.
The perimeter of a rectangle is the sum of all its sides, which in this case is given as 342 yards. So, the equation becomes: 2(w + 3w + 3) = 342.
Simplifying this equation gives us: 8w + 6 = 342. Solving for 'w', we find that the width is 42 yards. Plugging this value back into the equation, we can find the length: 3(42) + 3 = 129 yards. Therefore, the dimensions of the rectangular playing field are 42 yards by 129 yards.