A new Youth Sports Center os being built in Hadleyville. The perimeter of the rectangular playing field is 462 yards. The length of the field is 9 yards less than quadrupled the width. What are the dimensions of the playing field?

Answer 1

Let's assume the width of the playing field is x yards.
According to the information given, the length of the field is 9 yards less than quadrupled the width, which is 4x - 9 yards.
The perimeter of a rectangle is given by the formula: P = 2(l + w).
Plugging in the given information, we can write the equation as follows:
462 = 2(4x - 9 + x)
462 = 2(5x - 9)
462 = 10x - 18
10x = 480
x = 480/10
x = 48
So, the width of the field is 48 yards.
The length of the field is 4x - 9 = 4(48) - 9 = 192 - 9 = 183 yards.
Therefore, the dimensions of the playing field are 48 yards by 183 yards.