In a single slit diffraction pattern, the angular position of the first minimum is given by the condition $a \sin\theta = \lambda$. For small angles, $\sin\theta \approx \tan\theta = \frac{y}{D}$, where $y$ is the linear distance of the first minimum from the centre of the central maximum on the screen, and $D$ is the distance of the screen from the slit. Substituting this, we get $a\left(\frac{y}{D}\right) = \lambda \implies y = \frac{D\lambda}{a}$. The central maximum lies between the first minima on both sides. Therefore, the total linear width of the central maximum is $2y = \frac{2D\lambda}{a}$.