Answer
The answer is $H$.
Work Step by Step
In similar triangles, corresponding sides are proportional to one another, so let's set up a proportion to compare two sides of one triangle to two sides of another triangle:
$\frac{6}{15} = \frac{3}{y}$
We want to find the shortest side of the larger triangle, which is $y$.
Use the cross products property to get rid of the fractions:
$6y = 45$
Divide each side of the equation by $6$ to solve for $y$:
$y = 7.5$ in.
The answer is $H$.
