We need to find a different pair of length and width, l_2 and w_2, such that their sum is 12 cm (since 2(l_2 + w_2) = 24 cm). We can choose any two positive numbers that add up to 12, as long as they are different from 8 and 4. For example, we can choose l_2 = 10 cm and w_2 = 2 cm.

We need to find a different pair of length and width, l_2 and w_2, such that their sum is 12 cm (since 2(l_2 + w_2) = 24 cm). We can choose any two positive numbers that add up to 12, as long as they are different from 8 and 4. For example, we can choose l_2 = 10 cm and w_2 = 2 cm.

For the second rectangle with dimensions l_2 = 10 cm and w_2 = 2 cm, its area is 10 cm × 2 cm.

Comparing the areas, 32 cm² for the first rectangle and 20 cm² for the second rectangle, we see that the first rectangle has a larger area.

Two rectangles have the same perimeter of 24 cm. One of them is 8 cm by 4 cm. Give the dimensions of a different rectangle with the same perimeter, and compare the areas of the two rectangles.

Answer: A different rectangle with the same perimeter of 24 cm could have dimensions of 10 cm by 2 cm. The area of the first rectangle is 32 cm $^2$ , and the area of the second rectangle is 20 cm $^2$ . The first rectangle has a larger area.

Step-by-step solution

Step 1: Calculate the perimeter of the first rectangle

The perimeter of a rectangle is calculated using the formula $P = 2(l + w)$ , where $l$ is the length and $w$ is the width. For the first rectangle, the given dimensions are $l_1 = 8 \text{ cm}$ and $w_1 = 4 \text{ cm}$ .

Step 2: Verify the perimeter of the first rectangle

Substitute the given length and width into the perimeter formula. This confirms that the perimeter of the first rectangle is indeed $24 \text{ cm}$ , as stated in the problem.

Step 3: Find dimensions of a different rectangle with the same perimeter

We need to find a different pair of length and width, $l_2$ and $w_2$ , such that their sum is $12 \text{ cm}$ (since $2(l_2 + w_2) = 24 \text{ cm}$ ). We can choose any two positive numbers that add up to 12, as long as they are different from 8 and 4. For example, we can choose $l_2 = 10 \text{ cm}$ and $w_2 = 2 \text{ cm}$ .

Step 4: Calculate the area of the first rectangle

The area of a rectangle is calculated by multiplying its length and width. For the first rectangle, the area is $8 \text{ cm} \times 4 \text{ cm}$ .

Step 5: Calculate the area of the second rectangle

For the second rectangle with dimensions $l_2 = 10 \text{ cm}$ and $w_2 = 2 \text{ cm}$ , its area is $10 \text{ cm} \times 2 \text{ cm}$ .

Step 6: Compare the areas

Comparing the areas, $32 \text{ cm}^2$ for the first rectangle and $20 \text{ cm}^2$ for the second rectangle, we see that the first rectangle has a larger area.

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