Question

An aquarium holding African cichlids is 2 inches higherthan it is wide. Its length is 32 inches, and its volume is11520 cubic inches.What are the height and width of the aquarium?Height =inchesWidth = inches

Answer 1

It is given that

An aquarium holding African cichlids is 2 inches higher than it is wide. Its length is 32 inches, and its volume is 11520 cubic inches.

Let w be the width of the aquarium.

The height =(w+2) inches

The volume of the aquarium is

`V=\text{width}* length* height`

Substitute width=w, height=w+2, length=32 and V=11520, we get

`11520=w*(w+2)*32`

`11520=32w(w+2)`

`11520=32w^2+2*32w`

`11520=32w^2+64w`

Transferring 11520 to the right-hand side, we get

`32w^2+64w-11520=0`

Dividing by 32, we get

`(32w^2)/(32)+(64w)/(32)-(11520)/(32)=(0)/(32)`

`w^2+2w-360=0`

`w^2+20w-18w-360=0\text{ }`

`w(w+20)-18(w-20)=0\text{ }`

`(w+20)(w-18)=0\text{ }`
`(w+20)=0\text{ or }(w-18)=0`

`w=-20\text{ or }w=18`

The measure of side should be positive

We take w=18.

Hence width w=18 inches

Height=w+2=18+2=20 inches .