You have been asked to construct an aquarium that holds 1000 gallons. it will be a standard rectangular prism with restrictions that the length must be 1 foot longer than the width and the height must be 4.6 feet less than the length. find the height of the aquarium to the nearest hundredth of an inch.

The height of the aquarium is

Step-by-step explanation:

Remember that

we know that

The volume of a rectangular prism is equal to

In this problem we have

so

----> equation A

--->  --->equation B (convert ft to in)

---> ---> equation C (convert ft to in)  

substitute equation B and equation C in equation A

solve for L

Apply distributive property

Solve the cubic equation by graphing

using a graphing tool

The solution is L=88.95 in

see the attached figure

Find the height of the aquarium H

substitute the value of L

Find the value of W  

or