To solve the problem, we first need to determine the area of the initial rectangle and then use that area to find the length of the second rectangle with a width of 7 cm.

Step 1: Calculate the area of the first rectangle.

The area $A$ of a rectangle is given by: $A = \text{length} \times \text{width}$

For the first rectangle:

• Length = 6 cm
• Width = 4 cm

$A = 6 \times 4 = 24 \, \text{cm}^2$

Step 2: Determine the length of the second rectangle.

Given that the area of the second rectangle is also 24 cm² and its width is 7 cm, we can find the length $L$ using the formula: $L = \frac{A}{\text{width}}$

$L = \frac{24}{7} \approx 3.43 \, \text{cm}$

Step 3: Draw the rectangles

• First Rectangle: A rectangle with a length of 6 cm and a width of 4 cm.
• Second Rectangle: A rectangle with a width of 7 cm and a length of approximately 3.43 cm, both having the same area of 24 cm².

Would you like to see a visual representation of these rectangles? If you need any more details, feel free to ask!

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Here are five questions related to this problem:

1. How would the area change if the first rectangle's width were doubled?
2. What would the new width be if we kept the area of 24 cm² and the length at 5 cm?
3. How would you calculate the perimeter of both rectangles?
4. Can you think of a rectangle with the same perimeter as the first rectangle but a different area?
5. What happens to the area if both the length and width of a rectangle are doubled?

Tip: When solving for the length or width of a rectangle with a known area, always ensure the other dimension is accurately measured or calculated.