A thin uniform square lamina of side a is placed in the xy-plane with its sides parallel to x and y-axes and with its center coinciding with origin. Its moment of inertia about an axis passing through a point on the y-axis at a distance $y=2a$ and parallel to x-axis is equal to its moment of inertia about an axis passing through a point on the x-axis at a distance $x=d$ and perpendicular to xy-plane. Then value of d is :

Question

$$\begin {array} {1 1} (a)\;\frac{7}{3}a & \quad (b)\;\frac{\sqrt {47}}{12}a \\ (c)\;\frac{9}{5}a & \quad (d)\;\frac{\sqrt {51}}{12} a \end {array}$$