The perimeter is the total of adding all the side lengths together.
The perimeter of a rectangle is:
P = L + L + w + w
or
P = 2L + 2w
The length of the rectangle is 6 times longer than the width, so:
L = 6w
To find the width, you can substitute 6w for L:
P = 2L + 2w
P = 2(6w) + 2w
P = 12w + 2w
P = 14w
[tex]\frac{P}{14} =w[/tex]