https://file.aiquickdraw.com/mathbot/file/17308327997766vhvnk2g.jpg

To solve for \( x \) in the right triangle, we can use the properties of similar triangles. Since the triangles in the image are similar, the corresponding sides are proportional. 

Given dataTo solve for \( x \) in the right triangle, we can use the properties of similar triangles. Since the triangles in the image are similar, the corresponding sides are proportional. 

Given 
- For the first triangle: the shorter leg is 25 in, the longer leg is 40 in, and the hypotenuse is 60 in.
- For the second triangle: the shorter leg is 20 in, the longer leg is \( x \), and the hypotenuse is 48 in.

Since the triangles are similar, the ratios of corresponding sides are equal.

Let's use the ratios of the longer legs and the shorter legs to set up a proportion.

\[
\frac{25}{20} = \frac{40}{x}
\]

Cross-multiplying to solve for \( x \):

\[
25 \cdot x = 20 \cdot 40
\]

\[
25x = 800
\]

\[
x = \frac{800}{25}
\]

\[
x = 32
\]

Thus, the solution is:

**c. 32 in.**

Would you like a detailed explanation of similar triangles or have any other questions?

Here are five additional related questions for further exploration:

1. How do you determine if two triangles are similar?
2. What are other methods to solve for missing sides in right triangles?
3. How can the Pythagorean theorem be applied in problems like these?
4. Why is proportional reasoning useful in geometry?
5. What are real-life applications of similar triangles?

**Tip:** When working with similar triangles, always identify corresponding sides carefully to set up correct proportions.

Solve for x in a pair of similar triangles with corresponding sides provided.

Understand how to solve for x in similar triangles by setting up proportions based on corresponding sides. This problem includes a detailed step-by-step solution using proportional reasoning and cross-multiplication, ideal 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