In the figure shown below, \(E\) and \(G\) lie on \(\overline{AC}\), \(D\) and \(F\) lie on \(\overline{AB}\), \(\overline{DE}\) and \(\overline{FG}\) are parallel to \(\overline{BC}\), and the given lengths are in feet. What is the length of \(\overline{AC}\), in feet?

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\(\triangle{ABC}\) is similar to \(\triangle{ADE}\). We can set up a proportion:

$$ \frac{AB}{AC} = \frac{AD}{AE} $$ $$ = \frac{8+7+6}{AC} = \frac{8}{16} $$ $$ \frac{21}{AC}=\frac{1}{2} $$ $$ AC = \boxed{42} $$