Question

the distance around a open (perimeter) a certain rectangular playing field is 310 M. The length is 65 meters more than the width. What are the length and width of the field?

Answer 1

The perimeter of the rectangular playing field is 310 m.

The length is 65 meters more than the width.

Let L represents the length and W represents the width of the playing field.

$L=65+W$

Recall that the perimeter of a rectangular shape is given by

$P=2(L+W)$

Substitute the value of perimeter and length into the above formula

$\begin{gathered} P=2(L+W) \\ 310=2(65+W+W) \\ 310=2(65+2W) \\ 310=130+4W \\ 310-130=4W \\ 180=4W \\ \frac{180}{4}=W \\ 45=W \\ W=45\: m \end{gathered}$

So, the width is 45 m.

$\begin{gathered} L=65+W \\ L=65+45 \\ L=110\: m \end{gathered}$

So, the length is 110 m.