Since the two triangular plots are similar, the corresponding sides are proportional.

Given the side lengths ratio of the first plot:

$9 : 12 : 15$

The shortest side of the first plot is $9$. The shortest side of the second plot is $18$ inches.

Step 1: Find the Scale Factor

The scale factor can be determined by comparing the shortest sides:

$\text{Scale factor} = \frac{\text{Shortest side of second plot}}{\text{Shortest side of first plot}} = \frac{18}{9} = 2$

Step 2: Determine the Length of the Longest Side

Since the scale factor is $2$, we multiply each side of the first plot by $2$ to find the corresponding sides of the second plot.

The longest side of the first plot is $15$, so the longest side of the second plot is:

$\text{Longest side of second plot} = 15 \times 2 = 30 \text{ inches}$

Thus, the correct answer is:

30.00 inches

Verification:

• Ratio of sides for the first plot: $9:12:15$
• Ratio of sides for the second plot: $18:24:30$
• Both ratios simplify to the same $3:4:5$, confirming similarity.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How do we find the scale factor between two similar geometric figures?
2. If the middle side of the second plot is 24 inches, how does it verify the proportional relationship?
3. What happens if the scale factor is not a whole number?
4. Can we determine the area of the second plot if we know the area of the first plot?
5. How do we confirm if two triangles are similar based on their sides?

Tip: When dealing with similar shapes, always check the scale factor by comparing corresponding sides.