To determine if the two rectangles are similar, we need to examine the ratio of their corresponding side lengths. Two rectangles are similar if their corresponding side lengths are proportional.

First Rectangle

• Length: 14
• Width: 10

Second Rectangle

• Length: 21
• Width: 15

Ratio of Corresponding Sides

We can compare the ratios of the corresponding lengths and widths:

1. Length ratio: $\frac{14}{21} = \frac{2}{3}$
2. Width ratio: $\frac{10}{15} = \frac{2}{3}$

Since both ratios are equal ($\frac{2}{3}$), the rectangles are similar. This is because they maintain the same proportional dimensions.

Would you like further details, or do you have any questions?

Here are five related questions to consider:

1. What other properties must two shapes have to be similar?
2. How do we prove similarity for polygons other than rectangles?
3. Can different shapes (like a rectangle and a square) ever be similar?
4. How does the concept of proportionality apply in scaling objects in geometry?
5. What are the implications of similarity in practical applications like map scaling?

Tip: When comparing two shapes for similarity, always simplify the ratios of their corresponding sides and ensure all ratios are equal.