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Jason cuts the large rectangle below into five smaller, congruent rectangles. The short side of the shaded rectangle has length 2 . What is the area of the large rectangle?




Let's analyze the problem and find the area of the large rectangle.

The large rectangle is divided into five smaller, congruent rectangles. The shaded rectangle is one of these smaller rectangles, and its short side has a length of 2 units.

To solve for the area of the large rectangle, we need to follow these steps:

1. Determine the dimensions of each smaller rectangle.
2. Use these dimensions to find the area of one smaller rectangle.
3. Multiply the area of one smaller rectangle by the number of smaller rectangles to get the area of the large rectangle.

Since the short side of the shaded rectangle is 2 units and all five smaller rectangles are congruent, let's denote:
- The short side (width) of each smaller rectangle as \( w = 2 \).
- The long side (height) of each smaller rectangle as \( h \).

We can see from the image that the large rectangle is formed by placing the five smaller rectangles in a vertical stack. This means the height of the large rectangle \( H \) is 5 times the height of one smaller rectangle \( h \), and the width \( W \) is the same as the width of one smaller rectangle \( w \).

Since \( w = 2 \):
\[ W = 2 \]

Now, we need to determine the height of the smaller rectangle \( h \).

From the image, it looks like the large rectangle is divided horizontally into 5 congruent smaller rectangles, which implies the following relationship:
\[ H = 5h \]

However, to solve for \( h \) and consequently for \( H \), we need additional information about the large rectangle or one of the other dimensions. Without this information, we can't determine the exact numerical values of \( h \) and \( H \).

Assuming the information provided is correct and interpreting that the height \( h \) is consistent for all smaller rectangles, we can assume the missing data to solve it if the length of the large rectangle is interpreted based on visual assumptions.

Therefore, without additional explicit information, the relationship holds:
\[ H = 5h \]
\[ W = 2 \]

Finally, the area \( A \) of the large rectangle is:
\[ A = W \times H \]
\[ A = 2 \times 5h \]
\[ A = 10h \]

Since \( h \) needs to be determined from more information which is not given, we interpret this relationship for determining area conceptually.

Would you like further details, or have any questions about this explanation? Here are 5 questions you might consider asking next:

1. How can we determine the height of each smaller rectangle with more detail?
2. What additional information can be derived from similar geometric problems?
3. How does the congruence property help in calculating the areas in geometry?
4. What if the large rectangle had different dimensional ratios?
5. Could we solve this using algebraic expressions if one more dimension was known?

**Tip:** Always double-check the given information and see if there are hidden clues in the problem statement or diagram to help in solving the problem accurately.

Learn how to calculate the area of a large rectangle divided into five congruent rectangles, with one rectangle having a known short side length of 2 units. Explore the geometric concept of division into congruent parts and its application in area calculation. Suitable for students in Grades 7-9.

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