Final answer:The dimensions of the rectangular playing field are found using algebraic expressions and the given perimeter. The width is calculated to be 53 yards, and the length is 108 yards.Explanation:To determine the dimensions of the rectangular playing field, we need to first represent the length and the width using algebraic expressions based on the information given in the question. Let the width of the playing field be represented as W (in yards). Then, according to the question, the length L (in yards) would be 2W + 2. The perimeter P of a rectangle is given by P = 2L + 2W. Substituting the expressions for L and W into the equation for the perimeter, and knowing that the perimeter is 322 yards, we have:322 = 2(2W + 2) + 2W322 = 4W + 4 + 2W322 = 6W + 4Now, subtracting 4 from both sides, we get:318 = 6WDividing both sides by 6 gives us the width:W = 53Now to find the length, we substitute W back into L = 2W + 2:L = 2(53) + 2L = 106 + 2L = 108Hence, the dimensions of the field are 108 yards in length and 53 yards in width....

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