Answer:
Given the statement: 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.
Since, aquarium is in the form of a rectangular solid.
Length of an aquarium(l) = 5 dm
Width of an aquarium(w)= [tex]\frac{4}{5}\times 5 = 4 dm[/tex]
It is also given that when you put 40 liters of water into the aquarium, it was full to [tex]\frac{2}{3}[/tex] its volume.
Volume of Rectangular solid(V) is given by;
[tex]V = l \times b \times h[/tex] where l is the length , w is the width and h is the height of the rectangle respectively.
Volume(V) of an aquarium = [tex]\frac{3}{2} \times 40 = 60[/tex] liter.
Using volume formula to calculate the height(h);
[tex]60 = 5 \times 4 \times h[/tex]
[tex]60 = 20h[/tex]
Divide both sides by 20 we get;
h = 3 dm [ 1 liter = 1 cubic dm]
We have to find the what part of length makes up the height of the aquarium.
[tex]h = \frac{3}{5} l[/tex] where l = 5 dm
therefore, [tex]\frac{3}{5}[/tex] part of the length makes up the height of the aquarium.
