SOLUTION: Find the length, width, and height of the rectangular prism with the given volume. Volume = 12 cubic inches H = x in. W = (x-1) in. L = (x=4) in. Please show your wo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the length, width, and height of the rectangular prism with the given volume. Volume = 12 cubic inches H = x in. W = (x-1) in. L = (x=4) in. Please show your wo      Log On


   

Question 1010402: Find the length, width, and height of the rectangular prism with the given volume.
Volume = 12 cubic inches
H = x in.
W = (x-1) in.
L = (x=4) in.
Please show your work and thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
height=xin
width=x-1in
length=x%2B4in
system%28Volume=height%2Awidth%2Alength%2CVolume=12in%5E3%29 ---> x%28x-1%29%28x%2B4%29=12
We need to solve the cubic equation x%28x-1%29%28x%2B4%29=12 .
x%28x-1%29%28x%2B4%29=12 <---> x%5E3%2B3x%5E2-4x=12 <---> x%5E3%2B3x%5E2-4x-12=0
We can solve it by factoring, because the problem was designed to yield an integer x value.
We factor by parts:
x%5E3%2B3x%5E2-4x-12=0
x%5E2%28x%2B3%29-4%28x%2B3%29=0
%28x%5E2-4%29%28x%2B3%29=0 ,
and then we factor further:
%28x-2%29%28x%2B2%29%28x%2B3%29=0 .
The solutions are:
x-2=0<-->x=2 ,
x%2B2=0<-->x=-2 , and
x%2B3=0<-->x=-3 .
We need a positive x , so highlight%28x=2%29--->highlight%28system%28x-1=1%2Cx%2B4=6%29%29 .
So, the length, width, and height of the rectangular prism are
highlight%28system%28length=6in%2Cwidth=1in%2Cheight=2in%29%29 .