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

2 answers:

6 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

mario62 [17]3 years ago

3 0

The height of the prism is 4 feet.

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