Answer:
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
Step-by-step explanation:
Given dimensions of a rectangular prism:
- Width = (2x - 2) ft
- Height = (x + 7) ft
- Area of the base = (3x² + 3x - 4) ft²
The area of the base of a rectangular prism is the product of the width of the base and the length of the base.
To determine if length b could be (3x - 1) ft, multiply b by the width of the base of the prism.
[tex]\begin{aligned}\implies \sf Area\;of\;base&=\sf length \times width\\&=b \times (2x-2)\\&=(3x-1)(2x-2)\\&=3x(2x-2)-1(2x-2)\\&=6x^2-6x-2x+2\\&=6x^2-8x+2\end{aligned}[/tex]
Therefore, the length of b cannot be (3x - 1) as the area of the base when b is (3x - 1) is not equal to the given area of the base.
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
