Answer:
The volume of the rectangular prism is [tex]45\ ft^3[/tex]
The volume of the triangular prism is [tex]35\ ft^3[/tex]
Step-by-step explanation:
step 1
Find the volume of the rectangular prism
The volume of rectangular prism is equal to
[tex]V=x(6)(3)[/tex]
[tex]Vrp=18x\ ft^3[/tex]
step 2
Find the volume of the triangular prism
The volume of triangular prism is equal to
[tex]V=\frac{1}{2} (4)(x)(7)[/tex]
[tex]Vtp=14x\ ft^3[/tex]
step 3
we know that
The volume of the rectangular prism is 10 cubic feet more than the volume of the right triangular prism
[tex]Vrp=Vtp+10[/tex]
substitute the given values and solve for x
[tex]18x=14x+10[/tex]
[tex]18x-14x=10[/tex]
[tex]4x=10[/tex]
[tex]x=2.5[/tex]
therefore
The volume of the rectangular prism is
[tex]Vrp=18x\ ft^3[/tex] -----> [tex]Vrp=18(2.5)=45\ ft^3[/tex]
The volume of the triangular prism is
[tex]Vtp=14x\ ft^3[/tex] -----> [tex]Vtp=14(2.5)=35\ ft^3[/tex]
