Question

The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter^3)

Answer 1

The height of aquarium is
`(3)/(5)` of its length

Explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium =
`(4)/(5)` of length

=
`(4)/(5) (5) = 4` decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is
`(2)/(3)` of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

`(2)/(3)` of volume of aquarium = 40

`(2)/(3)(20x)=40`

`(40x)/(3) =40`

multiply both side by 3

`40x= 3(40)`

`40x=120`

divide both side by 40

`x=(120)/(40)`

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

`(height )/(length) =(3)/(5)`

`height = (3)/(5) length`

hence the height of aquarium is
`(3)/(5)` of its length