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?
1 answer
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, $x = \boxed{12.5}.$