https://file.aiquickdraw.com/mathbot/file/1726522140810z09d6p7m.jpg

We are given that quadrilateral OPQR is similar to quadrilateral STUV, meaning that their corresponding sides are proportional. To solve for the measure of side ST, we will use the proportionality property of similar quadrilaterals.

### Step-by-step solution:
1. We are provided the following side lengths from the diagram:
   - \( OP = 12.1 \) (side of quadrilateral OPQR)
   - \( OR = 6 \) (side of quadrilateral OPQR)
   - \( SV = 24 \) (side of quadrilateral STUV)

2. We are asked to find the length of \( ST \), which is the side corresponding to \( OP \) in the smaller quadrilateral.

3. Since the quadrilaterals are similar, the ratio of the corresponding sides of the quadrilaterals should be equal. We can set up a proportion using the corresponding sides \( OP \) and \( ST \):
   \[
   \frac{ST}{OP} = \frac{SV}{OR}
   \]
   Plugging in the values we know:
   \[
   \frac{ST}{12.1} = \frac{24}{6}
   \]

4. Simplify the ratio on the right-hand side:
   \[
   \frac{24}{6} = 4
   \]

5. Now, solve for \( ST \):
   \[
   ST = 12.1 \times 4 = 48.4
   \]

Thus, the length of side \( ST \) is **48.4 units**.

Would you like further details or have any questions about this?

---

Here are five related questions:
1. What are other properties of similar quadrilaterals besides proportionality?
2. How can you confirm that two quadrilaterals are similar?
3. What is the ratio of perimeters between two similar quadrilaterals?
4. Can you use angles to check the similarity of quadrilaterals?
5. How do the areas of similar figures relate to the ratio of their corresponding sides?

**Tip:** Always verify the corresponding sides in similar figures carefully to avoid mistakes in setting up proportions.

Quadrilateral OPQR is similar to quadrilateral STUV. Find the measure of side ST. Figures are not drawn to scale.

Learn how to find the measure of side ST in quadrilateral STUV using similarity and proportionality. This problem covers key geometric concepts and is 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