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=(x^2+2x)/(x+1)`

Dimensions of the rectangular prism are:

`l=2x+4`

`w=(x)/(8)`

To find:

The height of the rectangular prism.

Solution:

The volume of a rectangular prism is:

`V=l* w* h`

After substituting the values, we get

`(x^2+2x)/(x+1)=(2x+4)* (x)/(8)* h`

`(x(x+2))/(x+1)=(2x(x+2))/(8)* h`

`(x(x+2))/(x+1)* (8)/(2x(x+2))=h`

`(1)/(x+1)* (8)/(2)=h`

`(4)/(x+1)=h`

Therefore, the correct option is C.