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.
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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 l1=8 cm and w1=4 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 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, l2 and w2, such that their sum is 12 cm (since 2(l2+w2)=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 l2=10 cm and w2=2 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 cm×4 cm.
Step 5: Calculate the area of the second rectangle
For the second rectangle with dimensions l2=10 cm and w2=2 cm, its area is 10 cm×2 cm.
Step 6: Compare the areas
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.