Question

The height of a rectangular prism is found by dividing volume, V, by the base area, B. If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height? 3x + 5 – 3x – 7 + 3x + 5 + 3x – 7 –

Answer 1

Answer:

$(3x+5)+\frac{28}{2x-4}$

Step-by-step explanation:

Since,

The volume of a rectangular prism = Base area × Height,

Given,

Volume of the rectangular prism = $6x^2-2x+8$

Base area = 2x - 4

Let h be the height,

$\implies 6x^2-2x+8=(2x-4)h$

$\implies h = \frac{6x^2-2x+8}{2x-4}$

By long division ( shown below ),

$h=(3x+5)+\frac{28}{2x-4}$

Which is the required expression that represents the height.

Answer 2

Answer:

$(3x+5) + \frac{14}{x-2}$

Step-by-step explanation:

We are given the following information in the question:

Volume of rectangular prism =

$6x^2 - 2x + 8$

Area of base of prism =

$2x -4$

Formula:

$\text{Volume of Prism} = \text{Area of base}\times \text{Height of prism}\\\\\text{Height of prism} = \displaystyle\frac{\text{Volume of Prism} }{\text{Area of base}}$

Putting the values we, get,

$\text{Height of prism} = \displaystyle\frac{6x^2 - 2x +8}{2x-4} = \frac{2(3x^2-x+4)}{2(x-2)}= (3x+5) + \frac{14}{x-2}$

Hence, the height of the prism is given by the expression $(3x+5) + \frac{14}{x-2}$