Question 19
In $\triangle ABC$ with integer side lengths,
$$
\begin{aligned} \cos A &= \dfrac{11}{16}, \\ \cos B &= \dfrac{7}{8}, \\ \cos C &= -\dfrac{1}{4}. \end{aligned}
$$
What is the least possible perimeter for $\triangle ABC?$
$$
\begin{aligned} \cos A &= \dfrac{11}{16}, \\ \cos B &= \dfrac{7}{8}, \\ \cos C &= -\dfrac{1}{4}. \end{aligned}
$$
What is the least possible perimeter for $\triangle ABC?$