Answer:
width = 3ft
volume = 144 ft³
Step-by-step explanation:
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle. As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).
Given:
- a = height of aquarium = 12 ft
- b = diagonal of base
- c = top corner to opposite corner = 13 ft
[tex]\implies \sf 12^2+b^2=13^2[/tex]
[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]
[tex]\implies \sf b=5[/tex]
Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.
Given:
- a = length of aquarium = 4 ft
- b = width of aquarium
- c = diagonal of base = 5 ft
[tex]\sf \implies 4^2+b^2=5^2[/tex]
[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]
[tex]\sf \implies b=3[/tex]
Therefore, the width of the aquarium is 3 ft.
As the aquarium is modeled as a rectangular prism:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]
