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)
in.
1 answer
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.