Volume of Prism: Length & Width (y^3-y, y-1)

[Markg1997]

if a swimming pool has a volume of y^3-y and a height of y-1 then what is the length and width?

 

[Mentallic]

The volume of a prism is

$$V=lbh$$

And so in your case, $V=y^3-y$ and $h=y-1$ so plug these in, can you then figure out what l and b must be? Hint: Factorize.

 

[Markg1997]

I have it set up as:
y(y-1)(y+1)=lw(y-1) which I then divide by (y-1) to get
y(y+1)=lw and then I am stuck

 

[SteamKing]

I have it set up as:
y(y-1)(y+1)=lw(y-1) which I then divide by (y-1) to get
y(y+1)=lw and then I am stuck

Yer pool is either y units long and (y+1) units wide or (y+1) units long and y units wide. Without additional information, you can't tell which dimension is which.

 

[HallsofIvy]

That's assuming that all measurements are whole integers which was not given.

 

[Mentallic]

That's assuming that all measurements are whole integers which was not given.

This doesn't assume whole integers at all. y could be any real value greater than 1.