The area of rectangle $ABCD$ with vertices $A$(0, 0), $B$(0, 4), $C$($x$, 4) and $D$($x$, 0) is 28 square units. If $x > 0$, what is the value of $x$?
Plotting the points, we see that the dimensions of the rectangle are $x$ and $4$.  The area of the rectangle is $(\text{length})(\text{width})=4x$, so $4x=28$ and $x=\boxed{7}$. [asy]
size(5cm);
import graph;
defaultpen(linewidth(0.7)+fontsize(12));
real x = 7;
pair A=(0,0), B=(0,4), C=(x,4), D=(x,0);
pair[] dots = {A,B,C,D};
dot(dots);
draw(A--B--C--D--cycle);
xaxis(-2,9,Arrows(4));
yaxis(-2,7,Arrows(4));
label("$A$",A,SW);
label("$B$",B,NW);
label("$C$",C,NE);
label("$D$",D,SE);
label("$x$",(B+C)/2,N);
label("$4$",(C+D)/2,E);[/asy]