a rectangle has a perimeter of length + length + width + width.
L = length of the fence.
W = width of the fence.
so the perimeter will be L+L+W+W or 2L+2W or 2(L+W).
now, we know that 120 ⩽ 2(L+W).
we also know that 168 ⩾ 2(L+W)
and we also know that whatever the length is, is twice the width, or L = 2W.
[tex]\bf 120\le 2(L+W)\implies 120\le 2(2W+W)\implies 120\le 2(3W)
\\\\\\
120\le 6W\implies \cfrac{120}{6}\le W\implies \boxed{20\le W}\\\\
-------------------------------\\\\
168\ge 2(L+W)\implies 168\ge 2(2W+W)\implies 168\ge 2(3W)
\\\\\\
168\ge 6W\implies \cfrac{168}{6}\ge W\implies \boxed{28\ge W}\\\\
-------------------------------\\\\
20\le W \le 28[/tex]
