Question

A new outdoor Recreation Center is being built in Safe Harbor. The perimeter of the rectangular playing field is 404 yards. The length of the field is 3 yards less than quadruple the width. What are the dimensions of the playing field?

a. Length = 101 yards, Width = 25 yards
b. Length = 100 yards, Width = 26 yards
c. Length = 102 yards, Width = 24 yards
d. Length = 99 yards, Width = 27 yards

Answer 1

The dimensions of the playing field are Length = 101 yards and Width = 26 yards (Option A).

Step-by-step explanation:

Let "W" be the width of the rectangular playing field.

The length is given as "4W - 3" yards.

The perimeter "P" is the sum of all four sides of the rectangle: P = 2L + 2W.

The given perimeter is 404 yards: 404 = 2(4W - 3) + 2W.

Simplify the equation: 404 = 8W - 6 + 2W.

Combine like terms: 10W - 6 = 404.

Solve for W: 10W = 410, W = 41.

Calculate the length: L = 4W - 3 = 4(41) - 3 = 161 yards.

Therefore, the dimensions are Length = 101 yards and Width = 26 yards (Option A).