Michael wanted to make a quilt with an area of 42 square feet. What are its possible dimensions if they must be whole numbers? Which length and width makes the most sense for a quilt?
Factors of 42:
2 * 21
3 * 14
6 * 7
Think of the length and width of a bed. Which dimensions make the most sense?
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2*21
6*7
To find the possible dimensions of the quilt with an area of 42 square feet, we need to factorize 42 into its pairs of whole number factors.
The factors of 42 are:
1 * 42
2 * 21
3 * 14
6 * 7
So, the possible dimensions for the quilt are:
1. Length: 1 foot, Width: 42 feet
2. Length: 2 feet, Width: 21 feet
3. Length: 3 feet, Width: 14 feet
4. Length: 6 feet, Width: 7 feet
To determine which length and width make the most sense for a quilt, consider a few factors:
1. Practicality: Usually, a quilt with extremely long or wide dimensions may not be practical. So, we can eliminate 1 * 42 from the options.
2. Proportion: It's generally desirable for a quilt to have a balanced proportion. Since a quilt is typically rectangular, it is more aesthetically pleasing if the length and width have a reasonable ratio. The options remaining are 2 * 21, 3 * 14, and 6 * 7.
3. Personal preference: Ultimately, the most sensible dimensions for a quilt depend on personal preference. Some people may prefer larger dimensions, while others may prefer smaller ones.
Considering all these factors, the 3 * 14 dimensions (3 feet by 14 feet) or the 6 * 7 dimensions (6 feet by 7 feet) could make the most sense for a quilt, as they offer a more balanced proportion compared to the 2 * 21 dimensions. However, the final decision would depend on the specific requirements and preferences of Michael or the person making the quilt.