Question

The length of a new rectangular playing field is 3 yards longer than quadruple the width. If the perimeter of the rectangle is 526 yards, what are the dimensions?

a) Length = 133 yards, Width = 44 yards
b) Length = 134 yards, Width = 45 yards
c) Length = 135 yards, Width = 46 yards
d) Length = 136 yards, Width = 47 yards

Answer 1

The dimensions of the rectangular playing field are Length = 211 yards and Width = 52 yards.

Step-by-step explanation:

Let's let 'x' represent the width of the rectangle in yards. According to the problem, the length of the rectangle is 3 yards longer than quadruple the width, so the length can be represented as '4x + 3'.

Since the perimeter of a rectangle is equal to twice the sum of its length and width, we can set up the equation 2(width + length) = 526 and substitute the expressions for the width and length into the equation.

2(x + 4x + 3) = 526

2(5x + 3) = 526

10x + 6 = 526

10x = 520

x = 52

Therefore, the width of the rectangle is 52 yards, and the length is 4(52) + 3 = 211 yards. So, the dimensions of the rectangle are Length = 211 yards and Width = 52 yards.