https://file.aiquickdraw.com/mathbot/file/17294715444456jdxhybg.jpg

The image shows two rectangles, \(JKLM\) and \(WXYZ\), with dimensions indicated.

For rectangle \(JKLM\):
- \(MJ = 7\)
- \(ML = 3\)

For rectangle \(WXYZ\):
- \(ZW = h\)
- \(YZ = 10\)

The problem suggests that these two rectangles are similar (\(JKLM \sim WXYZ\)).

### Solution:
Since the rectangles are similar, their corresponding sides are proportional. This means we can set up the following proportion between the corresponding sides:

\[
\frac{MJ}{ZW} = \frac{ML}{YZ}
\]

Substituting the known values:

\[
\frac{7}{h} = \frac{3}{10}
\]

Now, solve for \(h\):

\[
7 \cdot 10 = 3 \cdot h
\]
\[
70 = 3h
\]
\[
h = \frac{70}{3} \approx 23.33
\]

So, \(h \approx 23.33\).

Let me know if you need more details or have further questions.

---

Here are five follow-up questions for deeper understanding:
1. What are the properties of similar figures?
2. How does the ratio of the sides relate to the areas of similar figures?
3. Can the same proportional relationship be used for triangles or other polygons?
4. How would the problem change if the shapes were not similar?
5. What are other examples of problems where similarity helps in geometry?

**Tip:** In similar figures, all corresponding angles are equal, and the lengths of corresponding sides are proportional.

Find the missing side length h for two similar rectangles JKLM and WXYZ given that MJ = 7, ML = 3, and YZ = 10.

Learn how to solve for the missing side length h of rectangle WXYZ using similarity properties with JKLM. This problem demonstrates key concepts in geometry, including proportionality of sides and similarity theorems. 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