Question

Independent Practice

Find the minimum and maximum possible areas for a rectangle with the following measured area.

6 in. × 9 in.


A.
40.0 in.2, 54 in.2


B.
53.5 in.2, 54.5 in.2


C.
40.5 in.2, 54.5 in.2


D.
46.75 in.2, 61.75 in.2

Answer 1

To find the minimum and maximum possible areas for a rectangle given its dimensions (6 in. × 9 in.), we first calculate the exact area:

Area = length × width = 6 in. × 9 in. = 54 in².

Since the problem refers to measured areas, we can assume there might be slight variations in the measurements that would result in a range of possible areas.

While the exact minimum and maximum aren't specifically provided in the context you've given, we can think about how measurement uncertainties (e.g., ±0.5 in) can affect the total area.

Let's explore potential ranges:

1. If both dimensions are increased by 0.5 in:
- New length = 6.5 in.
- New width = 9.5 in.
- Area = 6.5 in. × 9.5 in. = 61.75 in².

2. If both dimensions are decreased by 0.5 in:
- New length = 5.5 in.
- New width = 8.5 in.
- Area = 5.5 in. × 8.5 in. = 46.75 in².

Thus, the area could range from 46.75 in² to 61.75 in².

Based on these calculations, the correct answer would be:

**D. 46.75 in², 61.75 in²**.