Question

The perimeter of a rectangular field is 138 feet. If the length of the field is 28 feet more than the width, what is the length of the field (in feet)?___

Answer 1

Let $w$ be the width of the rectangle & $l$ be the length of the rectangle. We know that the formula for perimeter is $p=2l+2w$. Since the perimeter of the field is 138 feet, it follows that $138=2l+2w$
Also, it is given that $l=w+28$
Let us solve $138=2l+2w$ and $l=w+28$
Substitute $w+28$ in for $l$ in the first equation & solve for $w$ as shown below
$2l+2w=138$
$2(w+28)+2w=138$
$2w+56+2w=138$
$4w=138-56$
$4w=82$
$w=20.5$
Since $l=w+28$ ; it follws that $l=20.5+28$
$l=48.5$
The length of the field is 48.5 feet.