Question

The length of a new rectangular playing field is 8 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 576 yards, what are its dimensions?

Answer 1

• Width: 56 yards.

,

• Length: 232 yards.

Step-by-step explanation:

Let the width of the rectangular field = w

Quadruple the width = 4w

The length is 8 yards longer than quadruple the width. Therefore:

`\text{Length}=(4w+8)\text{ yards}`

The perimeter of the field is 576 yards.

`\begin{gathered} \text{Perimeter of a rectangle = 2(Length+Width)} \\ 576=2(4w+8+w) \end{gathered}`

We solve the equation for w.

`\begin{gathered} \text{Divide both sides by 2} \\ (576)/(2)=(2(4w+8+w))/(2) \\ 288=5w+8 \\ \text{Subtract }8\text{ from both sides} \\ 288-8=5w \\ 280=5w \\ \text{Divide both sides by }5 \\ (280)/(5)=(5w)/(5) \\ w=56\text{ yards} \end{gathered}`

The width of the rectangular playing field is 56 yards.

Next, we find the length.

`\begin{gathered} \text{Length}=(4w+8)\text{ yards} \\ =4(56)+8 \\ =224+8 \\ =232\text{ yards.} \end{gathered}`

The length of the rectangular playing field is 232 yards.