12.8×8 There is a 2D rectangle in which 10 rectangle have to be adjusted so what will be the length and breadth of 1 rectangle

To determine the length and breadth of each of the 10 rectangles that need to fit into a 12.8 × 8 rectangle, we can proceed as follows:

1. The total area of the large rectangle is:
\[ 12.8 \times 8 = 102.4 \text{ square units} \]

2. Since there are 10 smaller rectangles that need to fit into this larger rectangle, the area of each smaller rectangle must be:
\[ \frac{102.4}{10} = 10.24 \text{ square units} \]

We need to determine the dimensions (length and breadth) of the smaller rectangles such that their total area equals 10.24 square units and they can fit within the 12.8 × 8 rectangle. There are multiple possible configurations, but we'll consider the most straightforward one where all rectangles have the same dimensions.

To find possible dimensions:

Let's assume:
\[ \text{Length} = l \]
\[ \text{Breadth} = b \]

Given that:
\[ l \times b = 10.24 \]

We need to ensure that the arrangement of the 10 rectangles fits within the larger rectangle. One possible way to achieve this is by considering various aspect ratios. Here are a few possibilities:

### Option 1: Rectangles with equal dimensions
Let's assume \( l \) and \( b \) are equal (i.e., squares).
\[ l = b = \sqrt{10.24} \approx 3.2 \]

Thus, each smaller rectangle would be:
\[ 3.2 \times 3.2 \]

### Option 2: Rectangles with different length and breadth
Let's explore another set of dimensions:
Suppose the length is twice the breadth:
\[ l = 2b \]

Then:
\[ 2b \times b = 10.24 \]
\[ 2b^2 = 10.24 \]
\[ b^2 = 5.12 \]
\[ b \approx \sqrt{5.12} \approx 2.26 \]
\[ l = 2 \times 2.26 \approx 4.52 \]

Thus, each smaller rectangle would be:
\[ 4.52 \times 2.26 \]

These are two examples of possible dimensions. 

Would you like a detailed explanation or have any questions? Here are some related questions for further exploration:

1. How can we verify if a different set of dimensions fits within the 12.8 × 8 rectangle?
2. What is the maximum possible length of a rectangle if its breadth is fixed at 2 units?
3. Can the 10 rectangles be arranged differently, such as in a non-uniform pattern?
4. What happens if the large rectangle’s dimensions are changed?
5. How do the dimensions of the rectangles affect the perimeter of each smaller rectangle?
6. Can the dimensions of the smaller rectangles be fractional or must they be whole numbers?
7. What other geometric shapes can be used to divide the 12.8 × 8 rectangle into equal areas?
8. How does the aspect ratio of the smaller rectangles influence their arrangement within the larger rectangle?

**Tip:** When dividing a large area into smaller regions, always consider both the area and the perimeter constraints to ensure a proper fit.

Explore how to calculate the dimensions of 10 rectangles to fit into a larger 12.8 × 8 rectangle. Learn about area calculations and different dimension configurations. Suitable for students in Grades 7-9.

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