The rule of the volume of the rectangular prism is
[tex]V=L\times W\times H[/tex]
L is the length
W is the width
H is the height
Since the tank is 6 2/3 ft wide and 4 2/3 height, then
[tex]\begin{gathered} W=6\frac{2}{3}=\frac{6\times3+2}{3} \\ W=\frac{20}{3} \end{gathered}[/tex][tex]\begin{gathered} H=4\frac{2}{3}=\frac{4\times3+2}{3} \\ H=\frac{14}{3} \end{gathered}[/tex]
Since the volume of the tank is 350 cubic feet, then
[tex]V=350[/tex]
Substitute them in the rule above
[tex]\begin{gathered} 350=L\times\frac{20}{3}\times\frac{14}{3} \\ 350=\frac{280}{9}L \end{gathered}[/tex]
Divide both sides by 280/9 to find L
[tex]\begin{gathered} \frac{350}{\frac{280}{9}}=L \\ \frac{45}{4}=L \end{gathered}[/tex]
Make it a mixed number
Since 45/4 = 11 1/4
[tex]L=11\frac{1}{4}[/tex]
The length is 11 1/4 feet
