Answer
Length: $10$ inches
Width: $10$ inches
Work Step by Step
The dimensions of the box are:
$$\begin{align*}
&\text{Length:}& x\\
&\text{Width:}& x\\
&\text{Height:}& 2.
\end{align*}$$
We are given that its volume is $V=200$. We solve the equation $V=200$ for $x$:
$$\begin{align*}
x\cdot x\cdot 2&=200\quad&&\text{Write the given equation.}\\
x^2&=100\quad&&\text{Divide each side by }2.\\
x&=\pm 10\quad&&\text{Take the square root.}
\end{align*}$$
As $x$ is a dimension, it must be positive, so the only solution is $x=10$.
Calculate the dimensions of the box:
$$\begin{align*}
&\text{Length:}& x=10\\
&\text{Width:}& x=10\\
&\text{Height:}& 2.
\end{align*}$$
