Question

The perimeter of a rectangular fence is to be at least 120 feet and no more than 168 feet. If the length of the fence is to be twice the​ width, what is the range of values for the width of the​ fence?

Answer 1

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.

$\bf 120\le 2(L+W)\implies 120\le 2(2W+W)\implies 120\le 2(3W) \\\\\\ 120\le 6W\implies \cfrac{120}{6}\le W\implies \boxed{20\le W}\\\\ -------------------------------\\\\ 168\ge 2(L+W)\implies 168\ge 2(2W+W)\implies 168\ge 2(3W) \\\\\\ 168\ge 6W\implies \cfrac{168}{6}\ge W\implies \boxed{28\ge W}\\\\ -------------------------------\\\\ 20\le W \le 28$