Solution:
Given the figure labeled below:
A) Length A and Width B
In the above figure,
[tex]\begin{gathered} BC=VW+XY\text{ } \\ similarly, \\ AB=WX+YZ \end{gathered}[/tex][tex]\begin{gathered} where \\ BC=8 \\ VW=3 \\ XY=A \\ thus,8=3+A \\ subtract\text{ 3 from both sides} \\ 8-3=3-3+A \\ \Rightarrow A=5\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} Also, \\ AB=8 \\ WX=4 \\ YZ=B \\ thus, \\ 8=4+B \\ subtract\text{ 4 from both sides of the equation} \\ 8-4=4-4+B \\ \Rightarrow B=4\text{ ft.} \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} length\text{ A = 5 ft.} \\ width\text{ B= 4 ft.} \end{gathered}[/tex]
B) The volume of the water trough:
Since the water trough is made up of two rectangular prisms, we can split the figure into two rectangular prisms as shown below:
To calculate the volume,
step 1: Evaluate the volume of prism 1.
The volume of prism 1 is expressed as
[tex]\begin{gathered} Volume\text{ = base area}\times height \\ where \\ base\text{ area = length}\times width=4\text{ ft}\times3\text{ ft=12 ft}^2 \\ height=2\text{ ft} \\ thus, \\ Volume\text{ of prism 1 = 12 ft}^2\times2\text{ ft} \\ \Rightarrow Volume\text{ of prism 1 = 24 ft}^3 \end{gathered}[/tex]
step 2: Evaluate the volume of prism 2.
Similarly, the volume of prism 2 is evaluated as
[tex]\begin{gathered} Volume\text{ of prism 2= \lparen length}\times width)\times height \\ where \\ length=8\text{ ft} \\ width=4\text{ ft.} \\ height=2\text{ ft.} \\ thus, \\ volume\text{ of prism 2 =\lparen8 ft}\times4ft)\times2\text{ ft} \\ \Rightarrow volume\text{ of prism 2 = 64 ft}^3 \end{gathered}[/tex]
step 3: Sum up the volumes of prisms 1 and 2.
Thus, the volume of the water trough is evaluated to be
[tex]\begin{gathered} Volume\text{ of water trough = 24 ft}^3+\text{ 64 }ft^3 \\ \Rightarrow Volume\text{ of water trough = 88 }ft^3 \end{gathered}[/tex]
