A new youth activity center is being built in junction city. The perimeter of the rectangular playing field is 406 yards. The length of the field is 9 yards less than triple the width. What are the dimensions of the playing field?
Let's assume that the width of the playing field is "w" yards.
According to the problem, the length of the field is 9 yards less than triple the width, which can be expressed as:
Length = 3w - 9
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Substituting the values we have:
406 = 2(3w - 9 + w)
Simplifying the equation:
406 = 2(4w - 9)
406 = 8w - 18
8w = 406 + 18
8w = 424
w = 53
Therefore, the width of the playing field is 53 yards.
Using the equation for the length:
Length = 3w - 9
Length = 3(53) - 9
Length = 150
Therefore, the dimensions of the playing field are 150 yards by 53 yards.