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

`(3x+5) + (14)/(x-2)`

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}* \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(6x^2 - 2x +8)/(2x-4) = (2(3x^2-x+4))/(2(x-2))= (3x+5) + (14)/(x-2)`

Hence, the height of the prism is given by the expression
`(3x+5) + (14)/(x-2)`

Answer 2

`(3x+5)+(28)/(2x-4)`

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 = (6x^2-2x+8)/(2x-4)`

By long division ( shown below ),

`h=(3x+5)+(28)/(2x-4)`

Which is the required expression that represents the height.