jmc

Let the length of the rectangle be $l$ and the width be $w$. We are trying to find the area of the rectangle, or $l\cdot w$, so we need to first find both $l$ and $w$. We can set up the following system of equations to represent the given information:

$$\begin{array}{rl}l& =4w\\ 2l+2w& =100\end{array}$$

We will first solve for $w$ by eliminating $l$ from the equations above. Substituting the first equation into the second to eliminate $l$, we get $2(4w)+2w=100$ or $w=10$. Plugging this value into the first equation gives $l=4(10)=40$. Thus, the area of the rectangle is $l\cdot w=40\cdot 10=\boxed{400}$ square centimeters.