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A rectangular prism has a volume of 3x^2 + 18x + 24. Its base has a length of x + 2 and a width of 3. Which expression represents the height of the prism?
JMAP math geometry
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A rectangular prism has a volume of 3x2 + 18x + 24. Its base has a length of x + 2 and a width of 3. Which expression represents the height of the prism?

1) x + 4

2) x + 2

3) 3

4) x2 + 6x + 8

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judziy
Asked by judziyrep:1.4K
University of Benin Nigeria
11 June 2020

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peter
Peter answeredrep:1.4K
University of Lagos Nigeria
12 August 2020
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The volume of any prism can also be given as the base area of that prism multiplied by the height. That is,

Volume of prism = Area of base x Height of prism

for a rectangular base,

Area of base = Length x Width.

Thus, volume of the rectangular prism = Length x Width x Height

3x2 + 18x + 24 = (x + 2) * 3 * h

divide through by 3

x2 + 6x + 8 = (x + 2)h

Divid both sides by x+2

h = (x2 + 6x + 8) / (x + 2)

from division of polynomial, h = x + 4

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