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ollegr [7]
3 years ago
6

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)
Mathematics
1 answer:
NikAS [45]3 years ago
8 0

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.

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