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

$V=\text{width}\times length\times height$

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

$11520=w\times(w+2)\times32$

$11520=32w(w+2)$

$11520=32w^2+2\times32w$

$11520=32w^2+64w$

Transferring 11520 to the right-hand side, we get

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

Dividing by 32, we get

$\frac{32w^2}{32}+\frac{64w}{32}-\frac{11520}{32}=\frac{0}{32}$

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

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

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

$(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 .