# An American football field is a rectangle with a perimeter of 1040 fee. The length is 200 feet more than width. How do you find the width and the length of the rectangular field?

Mar 26, 2018

Width=160 ft
Length=360 ft

#### Explanation:

The perimeter of the field is the total distance around the rectangle, so it is given by: (Length times 2)+(Width times 2)

We know that the length is 200ft longer than the width, hence:
((Width+200) times 2)+(width times 2)=1040, the total perimeter.

This can also be expressed as:

$1040 = 2 \left(x + 200\right) + 2 \left(x\right)$

Where $x$ is the width of the field.

Solving for $x$:
$1040 = 2 x + 400 + 2 x$
$640 = 4 x$
$x = 160$

So the width is 160 ft.
We knew that the length was 200 ft longer to we just add 200 to the width: (160+200)=360 ft