The volume of the box-shaped a cuboid is
![V=l* w* h](https://img.qammunity.org/2023/formulas/mathematics/college/6r1v4jyudv1wid1xri6o6h85nmm0m84ukq.png)
l is the length
w is the width
h is the height
From the given figure
The volume of the box is 93 1/2 ft^3
V = 93 1/2
The width is 2 ft
w = 2
The height is 5 1/2 ft
h = 5 1/2
Substitute them in the rule above
![\begin{gathered} 93(1)/(2)=l*2*5(1)/(2) \\ (93*2+1)/(2)=l*2*(5*2+1)/(2) \\ (187)/(2)=l*2*(11)/(2) \\ (187)/(2)=l*11 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/vuymks11k3b6fljrfgwagqvsvkrb95tpz3.png)
Multiply both sides by 2 to remove the denominator
![187=22l](https://img.qammunity.org/2023/formulas/mathematics/college/pfncly9ffak52u1gs0npp5y0ozqgrf9u4p.png)
Divide both sides by 22 to find l
![\begin{gathered} (187)/(22)=(22l)/(22) \\ 8(1)/(2)=l \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/cdrya7f5mszrw16se61tjuvyvnpdx4j709.png)
The length of the box is 8 1/2 ft
The answer is B