Question

The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?

Answer 1

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.

Step-by-step 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) + 2W

322 = 4W + 4 + 2W

322 = 6W + 4

Now, subtracting 4 from both sides, we get:

318 = 6W

Dividing both sides by 6 gives us the width:

W = 53

Now to find the length, we substitute W back into L = 2W + 2:

L = 2(53) + 2

L = 106 + 2

L = 108

Hence, the dimensions of the field are 108 yards in length and 53 yards in width.

Answer 2

Step-by-step explanation:

First, we want to take the information we have and turn it into an equation, where x is our unknown dimension. For this problem, it would be better if x was equal to the width.

Let's write out the equation:

X is the width, 2x + 2 is the length, and we are multiplying both by two since there are two sides of the field. It will all equal to 322, because that is the perimeter.

2*x + 2(2x +2) = 322

Now, let's solve:

2*x + 2(2x + 2) = 322

2x + 4x + 4 = 322

6x + 4 = 322

6x = 318

x = 318 ÷ 6

x = 53

The width is 53 yards. To find the length, we multiply 53 by two and add two.

53 * 2 + 2 = 106 + 2 = 108 yards, as the length