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?

Answer 1

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.