Question

The volume of a rectangular prism is 6x3 + 25x2 + 21x − 10. The length of the prism is 2x + 5. The width of the prism is 3x − 1. What is an expression for the height of the prism?

Answer 1

Expression for the height of the prism is x + 2

Solution:

Given that,

`Volume\ of\ a\ rectangular\ prism = 6x^3+25x^2 + 21x - 10`

`Length\ of\ prism = 2x + 5`

`Width\ of\ prism = 3x-1`

To find: height of prism

The volume of rectangular prism is given by formula:

`Volume = length * width * height`

Solving for height we get,

`height = (volume)/(length * width)`

Substituting the values we get,

`height = (6x^3+25x^2+21x-10)/((2x+5)(3x-1))`

Factor the numerator

`height = ((x+2)(3x-1)(2x+5))/((2x+5)(3x-1))`

Cancel the common factors,

`height = x + 2`

Thus expression for the height of the prism is x + 2