Answer:
Part 1)
Part 2)
We can have the aquarium have a width of 40 inches, a height of 49 inches, and a length of 9 inches.
Or we can have the aquarium have a width of 21 inches, a height of 30 inches, and a length of 28 inches.
Step-by-step explanation:
The dimensions of the aquarium is as follows:
Part 1)
We want to find a polynomial expression that represents the volume of the aquarium according to the specified dimensions.
Since the aquarium is a rectangular prism, the volume will simply be the product of all the dimensions. Hence:
Part 2)
We want to aquarium to hold 17, 640 cubic inches of water. In other words, the volume V should be 17640. Thus:
First, we can distribute the right-hand side:
Distribute:
Distribute:
Simplify:
Now, we can factor. From the first two terms, factor out a -w² and from the second two terms, we can factor out 441:
Grouping:
Zero Product Property:
Solve for each case:
So, we have two possible sets of dimensions.
We can have the aquarium have a width of 40 inches, a height of 49 inches, and a length of 9 inches.
Or we can have the aquarium have a width of 21 inches, a height of 30 inches, and a length of 28 inches.