Since the two triangles are similar, their corresponding sides are proportional. The longest side of the first triangle is 5, and the longest side of the second triangle is 30. We can set up a proportion based on the longest sides of both triangles:

$\frac{\text{Longest side of first triangle}}{\text{Longest side of second triangle}} = \frac{\text{Shortest side of first triangle}}{\text{Shortest side of second triangle}}$

Substituting the known values:

$\frac{5}{30} = \frac{3}{x}$

Now, solve for $x$, the shortest side of the second triangle:

$5 \cdot x = 3 \cdot 30$

$5x = 90$

$x = \frac{90}{5} = 18$

Thus, the length of the shortest side of the second triangle is 18.

The correct answer is:

c) 18

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Would you like to go over any details or have additional questions? Here are five related questions for further exploration:

1. How would you calculate the perimeter of a similar triangle if you know the lengths of the sides?
2. What is the ratio of the areas of two similar triangles if their corresponding sides are in a ratio of 1:2?
3. How do you determine the scale factor between two similar shapes?
4. If the sides of a triangle are in the ratio 3:4:5, how can you confirm whether it is a right triangle?
5. How do you apply similar triangle properties to real-world problems, such as calculating the height of a building?

Tip: When working with similar triangles, always identify the corresponding sides and set up proportional relationships. This can simplify solving for unknown values.