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14 May, 06:25

A rectangular prism has a volume of 96 feet the area of the base is 24 feet what is the height of the prism

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Answers (2)
  1. 14 May, 07:30
    0
    The height of the prism is 4 feet.
  2. 14 May, 09:13
    0
    V=lhw

    x (x+8) (x-2) = 96

    x (x^2+6x-16) = 96

    x^3+6x^2-16x-96=0 this is true when x=4 so (x-4) is a factor ...

    (x^3+6x^2-16x-96) / (x-4)

    x^2 rem 10x^2-16x-96

    10x rem 24x-96

    24 rem 0

    (x-4) (x^2+10x+24) = 0

    (x-4) (x^2+4x+6x+24) = 0

    (x-4) (x (x+4) + 6 (x+4)) = 0

    (x-4) (x+6) (x+4) = 0

    x=-4,-6,4 since x>0 the only possible answer is

    x=4

    making the dimensions of the prism:

    L=12ft, W=4ft, H=2ft
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