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To determine if the two rectangles are similar, we need to compare the ratios of their corresponding sides.

1. **First Rectangle (NMLK):**
   - Length \( NK = 40 \, \text{in} \)
   - Width \( NM = 25 \, \text{in} \)

2. **Second Rectangle (WXYZ):**
   - Length \( WV = 48 \, \text{in} \)
   - Width \( WX = 30 \, \text{in} \)

For the rectangles to be similar, the ratio of the corresponding sides must be equal:

\[
\text{Ratio of lengths} = \frac{NK}{WV} = \frac{40 \, \text{in}}{48 \, \text{in}} = \frac{5}{6}
\]

\[
\text{Ratio of widths} = \frac{NM}{WX} = \frac{25 \, \text{in}}{30 \, \text{in}} = \frac{5}{6}
\]

Since both ratios are equal, the rectangles are indeed similar.

**Answer:** Yes, the shapes are similar.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. What does it mean for two shapes to be congruent?
2. How would you determine the similarity of two triangles?
3. What role do angles play in determining similarity?
4. How do you calculate the area of similar shapes?
5. Can non-rectangular shapes be similar? How would you check?

**Tip:** Remember that when checking for similarity in any shapes, it's crucial to compare the corresponding side ratios and ensure they are consistent across the entire shape.

Are these shapes similar? (Given two rectangles with dimensions 25 in by 40 in and 30 in by 48 in)

Explore the process of determining if two rectangles with dimensions 25 in by 40 in and 30 in by 48 in are similar. Learn about the concept of shape similarity in geometry, including the ratio of corresponding sides and the application of the Similarity Theorem. Suitable for students in Grades 6-8.

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