Two triangles used in an art project are similar. The sides of the smaller triangle have lengths of 6 in., 7 in., and 12 in. The perimeter of the larger triangle is 75 in. What is the length of the shortest side of the larger triangle?
The ratio of corresponding side lengths of two similar triangles is constant. Let $x$ be the length of the shortest side of the larger triangle, so we have the proportion $$ \frac{6}{x} = \frac{12}{75} = \frac{1}{x/6} = \frac{2}{75/6} = \frac{12.5}{x/12.5}. $$Therefore, $x = \boxed{12.5}.$
