Question

A new Community Wellness Complex is being built in Alston. The perimeter of the rectangular playing field is 476 yards. The length of the field is 2 yards less than quadruple the width. What are the dimensions of the playing field?

A) Length: 108 yards, Width: 22 yards
B) Length: 110 yards, Width: 24 yards
C) Length: 112 yards, Width: 26 yards
D) Length: 104 yards, Width: 20 yards

Answer 1

The dimensions of the playing field are Length: 190 yards, Width: 48 yards.

Step-by-step explanation:

Let's assume the width of the field is w yards. According to the problem, the length of the field is 2 yards less than quadruple the width, which means the length is 4w - 2 yards. The perimeter of a rectangle is given by the formula: P = 2(l + w). Since we are given the perimeter of the playing field as 476 yards, we can substitute the length and width into the formula and solve for the dimensions:

• 476 = 2((4w - 2) + w)
• 476 = 2(5w - 2)
• 476 = 10w - 4
• 480 = 10w
• w = 48

Substituting the value of w back into the expression for the length gives us:

• Length = 4(48) - 2 = 190

Therefore, the dimensions of the playing field are Length: 190 yards, Width: 48 yards. Hence, none of the given options are correct.