A rectangular box with a square base is 20 inches wider than it is tall. If x represents the width of the base of the box, then the volume of the box as a function of x is? ...

please help me with this problem (Nerd)

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- Jul 29th 2010, 06:14 PMcristinaivelisseVerbal Problem
A rectangular box with a square base is 20 inches wider than it is tall. If x represents the width of the base of the box, then the volume of the box as a function of x is? ...

please help me with this problem (Nerd)

- Jul 29th 2010, 06:35 PMeumyang
The volume of a rectangular prism is length * width * height.

$\displaystyle V = lwh$

You're given that the width is x.

Since the prism has a square base, the length is also x.

If the box is "20 inches wider than it is tall," then the height is the width minus 20 inches, or height = x - 20.

Put it all together you get

$\displaystyle \begin{aligned}

V &= lwh \\

&= x \cdot x \cdot (x - 20) \\

&= x^2(x - 20) \\

\end{aligned}$