https://file.aiquickdraw.com/mathbot/file/1727478540266u5mnvnuh.jpg

The problem shows two similar triangles, \( \triangle ABC \) and \( \triangle ADE \), and we need to find the length of the pond (represented by segment \( DE \)).

### Given Data:
- \( AB = 74 \, \text{ft} \)
- \( BC = 26 \, \text{ft} \)
- \( AC = 74 + 26 = 100 \, \text{ft} \) (total horizontal distance)
- \( AE = 185 \, \text{ft} \)

Since the triangles \( ABC \) and \( ADE \) are similar, the ratio of the corresponding sides should be equal. We can set up the proportion:

\[
\frac{AB}{AE} = \frac{BC}{DE}
\]

Substituting the known values:

\[
\frac{74}{185} = \frac{26}{DE}
\]

Now, we can solve for \( DE \):

\[
DE = \frac{26 \times 185}{74}
\]

Let me calculate that.The length of the pond, represented by \( DE \), is 65 feet.

Do you have any questions or need more details on how this was solved?

Here are 5 related questions to explore further:
1. What is the definition of similar triangles?
2. How do you find the ratio between the sides of two similar triangles?
3. How would the calculation change if \( AB \) and \( BC \) were different lengths?
4. How can you verify if two triangles are similar using angle properties?
5. What are other real-world applications of similar triangles?

**Tip:** When working with proportions, always make sure the corresponding sides are correctly identified to maintain accuracy.

If triangles ABC and ADE are similar in this diagram, what is the length of the pond?

Learn how to solve for the length of a pond by applying the concept of similar triangles and using proportions. In this problem, triangles ABC and ADE are similar, and we calculate the length of DE using given measurements of other triangle sides. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation