6. A shipping company has a rule that all packages must be rectangular prisms with a volume of no more than 9 cubic feet. What is the maximum measure for the height of the a box that has a width of 1.5 feet and a length of 3 feet?

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1. The volume $$ V $$ of a rectangular prism is given by the formula:
$$
V = \text{length} \times \text{width} \times \text{height}
$$

2. For the given box, the length is $$ 3 $$ feet, the width is $$ 1.5 $$ feet, and the height is $$ h $$ feet. Thus, the volume is:
$$
V = 3 \times 1.5 \times h = 4.5h
$$

3. The shipping company's rule states that the volume must be no more than $$ 9 $$ cubic feet:
$$
4.5h \leq 9
$$

4. Solve the inequality for $$ h $$:
$$
h \leq \frac{9}{4.5} = 2
$$

5. Thus, the maximum measure for the height of the box is:
$$
h = 2 \text{ feet}
$$
The maximum height of the box is 2 feet.

6. A shipping company has a rule that all packages must be rectangular prisms with a volume of no more than 9 cubic feet. What is the maximum measure for the height of the a box that has a width of 1.5 feet and a length of 3 feet?

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