The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.

Find the value of $r$.
Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.

Find the value of $r$.
Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.

Find the value of $r$.