In a single slit diffraction pattern, the angular spread of the central maximum is bounded by the first minima on either side. The condition for the first minimum is $a \sin \theta = \lambda$. Since $\theta$ is small, $\sin \theta \approx \theta = \frac{\lambda}{a}$. The angular width of the central maximum is $2\theta = \frac{2\lambda}{a}$. The linear width of the central maximum on a screen at a distance $D$ is given by $W = D(2\theta) = \frac{2D\lambda}{a}$.