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lesya692 [45]
3 years ago
10

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

Mathematics
2 answers:
ch4aika [34]3 years ago
6 0
V=lhw 

<span>x(x+8)(x-2)=96 </span>

<span>x(x^2+6x-16)=96 </span>

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

<span>(x^3+6x^2-16x-96)/(x-4) </span>
<span>x^2 rem 10x^2-16x-96 </span>
<span>10x rem 24x-96 </span>
<span>24 rem 0 </span>

<span>(x-4)(x^2+10x+24)=0 </span>

<span>(x-4)(x^2+4x+6x+24)=0 </span>

<span>(x-4)(x(x+4)+6(x+4))=0 </span>

<span>(x-4)(x+6)(x+4)=0 </span>

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

<span>x=4 </span>

<span>making the dimensions of the prism: </span>

<span>L=12ft, W=4ft, H=2ft</span>
mario62 [17]3 years ago
3 0
The height of the prism is 4 feet.
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