How does /usr/bin/time measure memory usage?

I didn't check source of time. But There are wait3 and wait4 functions for getting rusage of child process:

pid_t wait3(int *status, int options, struct rusage *rusage);
pid_t wait4(pid_t pid, int *status, int options, struct rusage *rusage);

struct rusage contains the maximum resident set size value.

Man page getrusage(2) describes the struct rusage.

I looked at the source (it's very short). It uses getrusage().