a. Explain how to decompose the large rec- tangle in Figure 12.3 into 2½ groups of 3½ squares, so as to describe the area of the rectangle as 21⁄2-3½-2 cm ²2 1 cm² Figure 12.3
a. Explain how to decompose the large rec- tangle in Figure 12.3 into 2½ groups of 3½ squares, so as to describe the area of the rectangle as 21⁄2-3½-2 cm ²2 1 cm² Figure 12.3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**6. a. Explanation of Decomposing a Rectangle**
In Figure 12.3, we have the task of decomposing a large rectangle into \(2 \frac{1}{2}\) groups of \(3 \frac{1}{2}\) squares, to express the area of the rectangle as:
\[
2 \frac{1}{2} \cdot 3 \frac{1}{2} \, \text{cm}^2
\]
**Figure 12.3 Details:**
- On the left, there is a small square labeled \(1 \, \text{cm}^2\).
- On the right, we see a larger rectangle composed of smaller squares. The layout is a grid with 5 columns and 3 rows, creating a total of 15 smaller squares inside the large rectangle.
These smaller squares illustrate how the large rectangle can be broken down into segments, helping in the understanding of its total area calculation using fractional groups and multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e650545-36a1-4f20-87dc-0658cb2bc972%2Ff9301b7a-85a6-44c3-9dc5-dd03c5df5bbe%2F1kzwx9a_processed.png&w=3840&q=75)
Transcribed Image Text:**6. a. Explanation of Decomposing a Rectangle**
In Figure 12.3, we have the task of decomposing a large rectangle into \(2 \frac{1}{2}\) groups of \(3 \frac{1}{2}\) squares, to express the area of the rectangle as:
\[
2 \frac{1}{2} \cdot 3 \frac{1}{2} \, \text{cm}^2
\]
**Figure 12.3 Details:**
- On the left, there is a small square labeled \(1 \, \text{cm}^2\).
- On the right, we see a larger rectangle composed of smaller squares. The layout is a grid with 5 columns and 3 rows, creating a total of 15 smaller squares inside the large rectangle.
These smaller squares illustrate how the large rectangle can be broken down into segments, helping in the understanding of its total area calculation using fractional groups and multiplication.
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