The first statement that the perimeter of a triangle is always more than the sum of its median is correct. For the second statement, consider the following figure:
In Δ ABD: AB+BD > AD ...(1) In ΔABD : DC + AC > AD ...(2) Adding (1) and (2), we get: AB + BD + DC + AC > 2AD ⇒ AB + BC + AC > 2AD Thus, the second statement is alsocorrect.