Question

using $v = lwh$, what is an expression for the volume of the following prism? image of a rectangular prism with dimensions: length $\frac{d - 2}{3d - 9}$, width $\frac{4}{d - 4}$, height $\frac{2d - 6}{2d - 4}$ multiple choice options: $\frac{4}{3d - 12}$, $\frac{4d - 8}{3(d - 4)^2}$, $\frac{1}{3d - 3}$, $\frac{4(d - 2)}{3(d - 3)(d - 4)}$

Explanation:

Step1: Identify length, width, height

Length \( l = \frac{d - 2}{3d - 9} \), Width \( w = \frac{4}{d - 4} \), Height \( h = \frac{2d - 6}{2d - 4} \)

Step2: Simplify each term

Simplify \( 3d - 9 = 3(d - 3) \), \( 2d - 6 = 2(d - 3) \), \( 2d - 4 = 2(d - 2) \)

Step3: Multiply \( l \times w \times h \)

$$
LATEXBLOCK0
$$

Answer:

\(\frac{4}{3d - 12}\) (the first option)