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 decimeter3)

of the height makes up the height.

Step-by-step explanation:

The length of an aquarium, which has the form of a rectangular solid, is

The width is of the length, so teh width is,

Let us assume the height is 'h' dm.

So the volume will be,

As 1 liter of water occupies volume of  1 dm³, so volume of 40 liters of water will be,

This is the th of total volume.

Hence total volume will be,

Therefore,

So the part of length makes up to the height will be,

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

it is c, trust i got your back lol

step-by-step explanation: