Question

13. Given the volume, V, of the rectangular prism below, find h, the height of the prism. V = (x ^ 2 + 2x)/(x + 1) l= 2x + 4 w= x/8
A.16(x + 1)
B.16/(x + 1)
C.4/(x + 1)
D. 4(x + 1)

Answer 1

Given:

Volume of a rectangular prism is:

$V=\dfrac{x^2+2x}{x+1}$

Dimensions of the rectangular prism are:

$l=2x+4$

$w=\dfrac{x}{8}$

To find:

The height of the rectangular prism.

Solution:

The volume of a rectangular prism is:

$V=l\times w\times h$

After substituting the values, we get

$\dfrac{x^2+2x}{x+1}=(2x+4)\times \dfrac{x}{8}\times h$

$\dfrac{x(x+2)}{x+1}=\dfrac{2x(x+2)}{8}\times h$

$\dfrac{x(x+2)}{x+1}\times \dfrac{8}{2x(x+2)}=h$

$\dfrac{1}{x+1}\times \dfrac{8}{2}=h$

$\dfrac{4}{x+1}=h$

Therefore, the correct option is C.