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

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Answer 1

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**.