Fiona plans to make a box in the shape of a rectangular prism for storing her outdoor checkers pieces and the
checker board. In order to fit all of the pieces, the box will need to have a volume of 96 cubic feet. The place she
needs to store it only has a height of 2 feet. She comes up with two different designs for the box. One of the
designs has dimensions of:
2 feet high by 6 feet wide by 8 feet long
A. What could be the dimension, in feet, of Fiona's other box design? Why does this meet Fiona's
requirements? (Hint: The volume of a rectangular prism is lwh.) SHOW and EXPLAIN your work.
Dimensions of other box design:

see the explanation

Step-by-step explanation:

we know that

The volume of the rectangular prism is given by

The box will need to have a volume of 96 cubic feet and a height of 2 feet

so

First design

we have

substitute the values

The first design meet Fiona's  requirements

Second design

we have

substitute in the formula

Solve for (LW)

The area of the base must be equal to 48 square feet

We could have the following dimensions for L and W (the volume and the height are given)

12 feet by 4 feet ----> the base's area is equal to 48 square feet

16 feet by 3 feet ----> the base's area is equal to 48 square feet

2 feet by 24 feet ----> the base's area is equal to 48 square feet

4√3 feet by 4√3 --->  the base's area is equal to 48 square feet

All the above dimensions meet Fiona's  requirements

therefore

The dimensions of the second design could be

2 feet high by 4 feet wide by 12 feet long

2 feet high by 3 feet wide by 16 feet long

2 feet high by 2 feet wide by 24 feet long

2 feet high by 4√3 feet wide by 4√3 feet long

y=mx+b

step-by-step explanation:

m slope

b y-intercept