The perimeter of a rectangle is computed as follows
perimeter = 2l + 2w
where l is the length and w the width.
The difference between the length and width of the rectangle is 7 yards means:
l - w = 7
or
l = 7 + w
Replacing this equation into perimeter's equation, we get:
perimeter = 2(7 + w) + 2w
perimeter = 2(7) + 2(w) + 2w distributing
perimeter = 14 + 4w combining similar terms
The perimeter is 38 yards, then
38 = 14 + 4w
38 - 14 = 14 + 4w - 14 subtracting 14 at both sides
24 = 4w
24/4 = 4w/4 dividing by 4 at both sides
6 = w
l = 7 + w
l = 7 + 6
l = 13
The length is 13 yards and the width is 6 yards
