Given:
Length of the rectangular prism = [tex]\dfrac{d-2}{3d-9}[/tex]
Width of the rectangular prism = [tex]\dfrac{4}{d-4}[/tex]
Height of the rectangular prism = [tex]\dfrac{2d-6}{2d-4}[/tex]
To find:
The volume of the rectangular prism.
Solution:
We know that the volume of rectangular prism is:
[tex]V=l\times w\times h[/tex]
Where, l is the length, w is the width and h is the height.
After substituting the given values, we get
[tex]V=\dfrac{d-2}{3d-9}\times \dfrac{4}{d-4}\times \dfrac{2d-6}{2d-4}[/tex]
[tex]V=\dfrac{d-2}{3(d-3)}\times \dfrac{4}{d-4}\times \dfrac{2(d-3)}{2(d-2)}[/tex]
[tex]V=\dfrac{(d-2)\times 4\times 2(d-3)}{3(d-3)\times (d-4)\times 2(d-2)}[/tex]
Cancel out the common factors.
[tex]V=\dfrac{4}{3\times (d-4)}[/tex]
[tex]V=\dfrac{4}{3(d-4)}[/tex]
[tex]V=\dfrac{4}{3d-12}[/tex]
Therefore, the correct option is C.
