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:

$Volume = length \times width \times height$

Solving for height we get,

$height = \frac{volume}{length \times width}$

Substituting the values we get,

$height = \frac{6x^3+25x^2+21x-10}{(2x+5)(3x-1)}$

Factor the numerator

$height = \frac{(x+2)(3x-1)(2x+5)}{(2x+5)(3x-1)}$

Cancel the common factors,

$height = x + 2$

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