jmc

Let $w$ be the width of each of the identical rectangles. Since $PQ=3w$, $RS=2x$ and $PQ=RS$ (because $PQRS$ is a rectangle), then $2x=3w$, or $$w=\frac{2}{3}x.$$ Therefore, the area of each of the five identical rectangles is $$x\left(\frac{2}{3}x\right)=\frac{2}{3}{x}^2.$$ Since the area of $PQRS$ is 4000 and it is made up of five of these identical smaller rectangles, then $$5\left(\frac{2}{3}{x}^2\right)=4000$$ or $$\frac{10}{3}{x}^2=4000$$ or $x^2=1200$ or $x\approx 34.6$ which, when rounded off to the nearest integer, is $\boxed{35}.$