https://file.aiquickdraw.com/mathbot/file/1727216756411hi727pp9.jpg

The image shows a problem where two pentagons \( STUVW \) and \( HIJFG \) are similar figures. The goal is to find the side lengths \( UV \) and \( TU \), given that the corresponding sides between the two shapes are proportional.

From the image:

- \( TU = 7 \)
- \( UV = 8 \)
- \( IJ = 30 \)
- \( JH = 35 \)
- \( HG = 50 \)
- Corresponding sides are labeled between \( STUVW \) and \( HIJFG \).

### Step-by-Step Solution:

Since the two figures are similar, their corresponding side lengths are proportional. We need to find the proportional relationship between the sides of \( STUVW \) and \( HIJFG \). For this, we use the ratio of corresponding known sides.

1. Corresponding sides:
   - \( TU \) corresponds to \( HI \)
   - \( UV \) corresponds to \( IJ \)
   
   The ratio of similarity can be found by comparing the known sides of the two shapes:
   \[
   \text{Ratio} = \frac{HI}{TU} = \frac{30}{7}
   \]

2. Using this ratio, we can find \( UV \) and \( TU \).

   For \( UV \):
   \[
   \frac{UV}{IJ} = \frac{TU}{HI} = \frac{8}{30}
   \]
   Solve for \( UV \).

   For \( TU \), the same ratio can be applied.

Once you apply these, you'll find the values of \( UV \) and \( TU \).

Let me know if you'd like further details on how to proceed or any questions.

### Related Questions:
1. How do you calculate the ratio of corresponding sides in similar figures?
2. How do you verify that two shapes are similar based on side lengths?
3. What happens if one of the side lengths is missing in a similar figure problem?
4. How do you solve for unknown angles in similar figures?
5. What is the role of proportionality in scaling similar figures?

**Tip:** When dealing with similar figures, always ensure the sides you are comparing correspond correctly between the two shapes.

Learn how to find missing side lengths in similar pentagons using proportions. This problem involves solving for UV and TU in pentagons STUVW and HIJFG, focusing on key geometric concepts such as proportionality and side length ratios. 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