The area of a rectangular space is 128 square feet. What are the possible pairs of whole number dimensions in feet?
4 * 32
8 * 16
area of rectangle is length x width. Therefore, we list all the factors of 128 in pairs:
1 x 128
2 x 64
4 x 32
8 x 16
Thanks, Jai. I missed the two obvious answers.
To find the possible pairs of whole number dimensions for a rectangular space with an area of 128 square feet, we need to look for factors of 128.
1. Start by finding the square root of 128.
- The square root of 128 is approximately 11.31.
2. Since we are looking for whole number dimensions, let's round down the square root to the nearest whole number, which is 11.
3. Now, start dividing 128 by decreasing numbers, starting from 11 and moving downwards, until you find a pair of factors (dimensions) that give an area of 128.
- Dividing 128 by 11 gives us approximately 11.63, which is not a whole number. So, 11 is not a factor.
- Dividing 128 by 10 gives us 12.8, which is not a whole number. Therefore, 10 is not a factor.
- Dividing 128 by 9 gives us approximately 14.22, which is not a whole number. Hence, 9 is not a factor.
- Dividing 128 by 8 gives us 16, which is a whole number. So, a pair of dimensions could be 8 feet by 16 feet.
- Dividing 128 by 7 gives us approximately 18.29, which is not a whole number. So, 7 is not a factor.
- Dividing 128 by 6 gives us approximately 21.33, which is not a whole number. Therefore, 6 is not a factor.
- Dividing 128 by 5 gives us 25.6, which is not a whole number. Hence, 5 is not a factor.
- Dividing 128 by 4 gives us 32, which is a whole number. So, another pair of dimensions could be 4 feet by 32 feet.
- Dividing 128 by 3 gives us approximately 42.67, which is not a whole number. So, 3 is not a factor.
- Dividing 128 by 2 gives us 64, which is a whole number. Hence, another pair of dimensions could be 2 feet by 64 feet.
4. Continuing to divide by decreasing numbers, we can see that there are no more whole number factors greater than or equal to 2.
To summarize, the possible pairs of whole number dimensions for a rectangular space with an area of 128 square feet are:
- 8 feet by 16 feet
- 4 feet by 32 feet
- 2 feet by 64 feet