Question 1065297
square prism means the base is a square.


the volume of a square prism is equal to s^2 * h.


s is the length of a side of the base.
h is the height.


he wants the height to be 2 feet less than the length and the width.


if the side length is equal to s, then the height must be equal to s-2


the volume is therefore equal to s^2 * (s-2).


set that equal to 3174 and your equation is 3174 = s^2 * (s-2)


simplify to get 3174 = s^3 - 2s^2


subtract 3174 from both sides of the equation and you get s^3 - 2s^2 - 3174 = 0.


i don't actually know how to solve that without graphing it, so that's what i did.


my equation to graph is y = x^3 - 2x^2 - 3174.


i looked for the point where that graph crosses y = 0.


that point is (15.394,0)


that's rounded to 3 decimal places, but it's close.


the length of the sides is 15.394 and the height of the sides is 13.394.


15.394^2 * 13.394 = 3174.046311 which is pretty close.


here's my graph:


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