A thin cylindrical rod of length $10 \mathrm{cm}$ is placed horizontally on the principal axis of a concave mirror of focal length $20 \mathrm{cm}$. The rod is placed in such a way that mid point of the rod is at $40 \mathrm{cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{\mathrm{x}}{3} \mathrm{cm}$. The value of $\mathrm{x}$ is _______.