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 point)
We know that the sides of similar triangles are proportional. Let the corresponding side lengths of the larger triangle be $6x$, $7x$, and $12x$, for some positive real number $x$. We are given that the perimeter of the larger triangle is $75$. Setting up an equation, we have $6x+7x+12x=75$. Combining like terms, we get $25x=75$, so $x=3$. Therefore, the length of the shortest side of the larger triangle is $6x = 6 \cdot 3 = \boxed{18}$ inches.
