6.5 feet

Explanation

The fence consists of posts separated by chain link so, for each chain link section, there's one post on each side. Because adjacent chain link sections share the post between them, each section will be the length of a post + the length of a chain section long.

In this problem, each post is 6 inches \({ (or \frac{1}{2}foot) }\) long and each chain section is 6 feet long making each post + chain section \({ 6\frac{1}{2} }\) feet long. But, because the fence must end with a post, we need one more post on the last section of the fence which adds another \({ \frac{1}{2} }\) foot to the total length.

The equation for the possible lengths of the fence then becomes \({ 6 \frac{1}{2}n + \frac{1}{2} }\) where n is the number of post + chain sections. So, of the possible answers, only 6.5 feet could not be the length of the fence because it would require n to be a fractional value (i.e. not a whole section of fence).

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