Consider two triangular plots of land that are similar in shape. The side lengths of the first plot are in the ratio of 9:12:15. For a second plot, which is also similar to the first, the shortest side measures 18 inches. To determine the length of the longest side of the second plot, calculate it to the nearest hundredth of an inch.

Consider two triangular plots of land that are similar in shape. The side lengths of the first plot are in the ratio of 9:12:15. For a second plot, which is also similar to the first, the shortest side measures 18 inches. To determine the length of the longest side of the second plot, calculate it to the nearest hundredth of an inch.

30.00

50.00

24.00

25.50

18.25

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.

Consider two triangular plots of land that are similar in shape. The side lengths of the first plot are in the ratio of 9:12:15. For a second plot, which is also similar to the first, the shortest side measures 18 inches. To determine the length of the longest side of the second plot, calculate it to the nearest hundredth of an inch.

Learn how to calculate the longest side of a triangular plot when given that the triangles are similar. The solution involves using ratios and proportions. For example, if the shortest side of one triangle is 18 inches, find the longest side of a similar triangle using a scale factor. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation