the perimeter of the rectangular playing field is 462 yards. The length of the field is 5 yards less than the triple width. What are the dimensions of the playing field.

P = 2L + 2W

462 = 2(3W - 5) + 2W

462 = 6W - 10 + 2W

462 = 8W - 10

462 + 10 = 8W

472 = 8W

59 = W

To find the dimensions of the rectangular playing field, we can use the given information about its perimeter and the relationship between its length and width.

Let's assume the width of the field is represented by "W" yards. According to the problem, the length of the field is 5 yards less than triple the width. Using this information, we can say that the length is equal to (3W - 5) yards.

Now, we know that the perimeter of a rectangle can be calculated by adding all four sides together. For a rectangle, the formula is: perimeter = 2(length + width).

Given that the perimeter of the playing field is 462 yards, we can set up an equation:

2((3W - 5) + W) = 462

Simplifying the equation, we get:

2(4W - 5) = 462

Expand:

8W - 10 = 462

Move the constant term to the other side:

8W = 462 + 10

8W = 472

Divide both sides by 8 to solve for W:

W = 472 / 8

W = 59

So, the width of the playing field is 59 yards.

To find the length, we substitute the value of W back into the equation:
Length = 3W - 5

Length = 3(59) - 5

Length = 177 - 5

Length = 172

Therefore, the dimensions of the playing field are 59 yards (width) and 172 yards (length).