To calculate the minimum and maximum possible areas for a rectangle with measured dimensions of 6 inches and 9 inches, we first calculate the nominal area:
Nominal area = length × width = 6 in. × 9 in. = 54 in².
Next, we need to consider measurement errors.
Assuming that there could be a small measurement error in each dimension (for example, ±0.5 inches), the dimensions could vary as follows:
- Minimum length: 6 in. - 0.5 in. = 5.5 in.
- Maximum length: 6 in. + 0.5 in. = 6.5 in.
- Minimum width: 9 in. - 0.5 in. = 8.5 in.
- Maximum width: 9 in. + 0.5 in. = 9.5 in.
Now let's calculate the minimum and maximum possible areas.
Minimum Area: Minimum area = minimum length × minimum width = 5.5 in. × 8.5 in. = 46.75 in².
Maximum Area: Maximum area = maximum length × maximum width = 6.5 in. × 9.5 in. = 61.75 in².
So, the minimum possible area is 46.75 in² and the maximum possible area is 61.75 in².
The correct answer is:
D. 46.75 in², 61.75 in².